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wandb/run-20251217_181044-gmt9ya4m/files/wandb-metadata.json

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+                ulysses_sequence_parallel_size: 1
+                use_orig_params: false
+                use_torch_compile: true
+                wrap_policy:
+                    min_num_params: 0
+            lora_alpha: 16
+            lora_rank: 0
+            path: Qwen/Qwen2.5-0.5B-Instruct
+            target_modules: all-linear
+            tokenizer_path: Qwen/Qwen2.5-0.5B-Instruct
+            trust_remote_code: false
+            use_remove_padding: false
+            use_shm: false
+        optim:
+            _target_: verl.workers.config.FSDPOptimizerConfig
+            betas:
+                - 0.9
+                - 0.999
+            clip_grad: 1
+            lr: 1e-05
+            lr_warmup_steps: -1
+            lr_warmup_steps_ratio: 0
+            min_lr_ratio: 0
+            num_cycles: 0.5
+            total_training_steps: 200
+            warmup_style: constant
+            weight_decay: 0.01
+        ppo_epochs: 1
+        ppo_max_token_len_per_gpu: 32768
+        ppo_micro_batch_size: null
+        ppo_micro_batch_size_per_gpu: 1
+        ppo_mini_batch_size: 32
+        profiler:
+            _target_: verl.utils.profiler.ProfilerConfig
+            all_ranks: false
+            enable: false
+            ranks: []
+            save_path: outputs/profile
+            tool: null
+            tool_config:
+                npu:
+                    _target_: verl.utils.profiler.config.NPUToolConfig
+                    analysis: true
+                    contents: []
+                    discrete: false
+                    level: level1
+                nsys:
+                    _target_: verl.utils.profiler.config.NsightToolConfig
+                    discrete: false
+                torch:
+                    _target_: verl.utils.profiler.config.TorchProfilerToolConfig
+                    step_end: null
+                    step_start: 0
+                torch_memory:
+                    _target_: verl.utils.profiler.config.TorchMemoryToolConfig
+                    stack_depth: 32
+                    trace_alloc_max_entries: 100000
+        rollout_n: 1
+        shuffle: false
+        strategy: fsdp
+        ulysses_sequence_parallel_size: 1
+        use_dynamic_bsz: false
+ctx_manager:
+    value:
+        generation:
+            gen_config:
+                kwargs: null
+                response_length: 400
+                temperature: 1
+                top_k: -1
+                top_p: 1
+custom_envs:
+    value:
+        Bandit:
+            env_config:
+                split: train
+            env_instruction: ""
+            env_type: bandit
+            max_actions_per_traj: 1
+            max_tokens: 100
+        BanditTest:
+            env_config:
+                split: test
+            env_instruction: ""
+            env_type: bandit
+            max_actions_per_traj: 1
+            max_tokens: 100
+        CoordFrozenLake:
+            env_config:
+                observation_format: grid_coord
+            env_instruction: You are solving the FrozenLake puzzle.\nForbid the whole and go to the target.\nYou may move to the unintended direction due to the slippery ice.\nExample answer format:\n<think>To forbid the hole and go to the target, I should go left then go up.</think>\n<answer>Left || Up</answer>\nA sample full output is as follows:\n<think>\n<observation>\n_O__\nO___\nG___\n__P_\n</observation>\nPlayer at (3,2); holes at (0,1) and (1,0); goal at (2,0). 1 Up move to safe ice\n(2,2). 2 Left slide to (2,1), adjacent to goal. 3 Left reach goal (2,0);\nplayer now on G.\n<prediction>\n_O__\nO___\n√\n___\n____\n</prediction>\n</think> \n<answer>Up || Left || Left</answer>
+            env_type: frozen_lake
+            max_actions_per_traj: 25
+            max_tokens: 120
+        CoordSokoban:
+            env_config:
+                dim_x: 6
+                dim_y: 6
+                max_steps: 100
+                num_boxes: 2
+                observation_format: grid_coord
+            env_instruction: "You are solving the Sokoban puzzle. You are the player and you need to push all boxes to targets.\nYou are provided with a symbol grid and the zero-indexed coordinates of the player, each box, and each target. \nCoordinates range from the top-left corner (0, 0) to the bottom-right corner (5, 5). \nWhen you are exactly next to a box, you can push it by moving in the same direction. \nYou cannot push a box through a wall, and you cannot pull a box.\nThe answer should be a sequence of actions, like <answer>Right || Right || Up</answer>.\n"
+            env_type: sokoban
+            max_actions_per_traj: 10
+            max_tokens: 120
+        Countdown:
+            env_config: null
+            env_instruction: 'You are solving the Countdown puzzle. You should use the num list to create an equation that equals the target. Example answer format: <think> To find an equation using [3, 5, 2] to get 4. Let''s check 2 + 5 = 7, 7 - 3 = 4. So the answer is 2 + 5 - 3 = 4. </think><answer>2 + 5 - 3</answer>'
+            env_type: countdown
+            max_actions_per_traj: 1
+            max_tokens: 100
+        FrozenLake:
+            env_config: null
+            env_instruction: 'You are solving the FrozenLake puzzle. Forbid the whole and go to the target. You may move to the unintended direction due to the slippery ice. Example answer format: <think>To forbid the hole and go to the target, I should go left then go up.</think><answer>Left || Up</answer>'
+            env_type: frozen_lake
+            max_actions_per_traj: 25
+            max_tokens: 100
+        LargerSokoban:
+            env_config:
+                dim_x: 8
+                dim_y: 8
+                max_steps: 100
+                num_boxes: 2
+                search_depth: 10
+            env_instruction: "You are solving the Sokoban puzzle. \nYou are the player and you need to push all boxes to targets. \nWhen you are right next to a box, you can push it by moving in the same direction. \nYou cannot push a box through a wall, and you cannot pull a box. \nThe answer should be a sequence of actions, like <answer>Right || Right || Up</answer>\n"
+            env_type: sokoban
+            max_actions_per_traj: 10
+            max_tokens: 100
+        Lean:
+            env_config: null
+            env_instruction: You are a Lean theorem prover. Given a Lean theorem statement, propose a sequence of tactics that completes the proof. Think step by step about which tactics to apply next. Provide tactics separated by '||', for example <answer>intro || simp || rfl</answer>.
+            env_type: lean
+            max_actions_per_traj: 30
+            max_tokens: 512
+        MediumSudoku:
+            env_config:
+                difficulty: medium
+                grid_size: 9
+                max_steps: 81
+                render_format: with_feedback
+                show_conflicts: true
+                show_valid_numbers: true
+            env_instruction: |
+                You are solving a Sudoku puzzle. Fill in the grid so that every row, column, and 3x3 box contains the numbers 1-9 without repetition.
+                Initial cells are shown in [brackets] and cannot be modified. Empty cells are shown as dots (.).
+                Place numbers one at a time using the format: <answer>place 5 at row 2 col 3</answer> or <answer>2,3,5</answer>
+                The environment will provide feedback on valid/invalid moves and show conflicts if any occur.
+            env_type: sudoku
+            max_actions_per_traj: 30
+            max_tokens: 150
+            max_workers: 32
+            parallel_friendly: false
+        MetamathQA:
+            env_config: null
+            env_instruction: 'You are solving Math problems. '
+            env_type: metamathqa
+            max_actions_per_traj: 1
+            max_tokens: 100
+        SimpleSokoban:
+            env_config:
+                dim_x: 6
+                dim_y: 6
+                max_steps: 100
+                num_boxes: 2
+            env_instruction: "You are solving the Sokoban puzzle. \nYou are the player and you need to push all boxes to targets. \nWhen you are right next to a box, you can push it by moving in the same direction. \nYou cannot push a box through a wall, and you cannot pull a box. \nThe answer should be a sequence of actions, like <answer>Right || Right || Up</answer>\n"
+            env_type: sokoban
+            max_actions_per_traj: 10
+            max_tokens: 100
+        SimpleSudoku:
+            env_config:
+                difficulty: easy
+                grid_size: 4
+                max_steps: 20
+                render_format: with_feedback
+                show_conflicts: false
+                show_valid_numbers: false
+            env_instruction: |
+                You are solving a Sudoku puzzle. Fill in the grid so that every row, column, and 2x2 box contains the numbers 1-4 without repetition.
+                Initial cells are shown in [brackets] and cannot be modified. Empty cells are shown as dots (.).
+                Place numbers one at a time using the format, for example: <answer>place 1 at row 2 col 3</answer> or <answer>1,2,3</answer>
+                The environment will provide feedback on valid/invalid moves and show conflicts if any occur.
+            env_type: sudoku
+            max_actions_per_traj: 20
+            max_tokens: 150
+            max_workers: 32
+            parallel_friendly: false
+        SokobanDifferentGridVocab:
+            env_config:
+                dim_x: 6
+                dim_y: 6
+                grid_lookup:
+                    "0": W
+                    "1": .
+                    "2": G
+                    "3": C
+                    "4": B
+                    "5": A
+                    "6": '@'
+                grid_vocab:
+                    .: empty
+                    '@': player on target
+                    A: player
+                    B: box
+                    C: box on target
+                    G: target
+                    W: wall
+                max_steps: 100
+                num_boxes: 1
+                search_depth: 30
+            env_instruction: "You are solving the Sokoban puzzle. \nYou are the player and you need to push all boxes to targets. \nWhen you are right next to a box, you can push it by moving in the same direction. \nYou cannot push a box through a wall, and you cannot pull a box. \nThe answer should be a sequence of actions, like <answer>Right || Right || Up</answer>\n"
+            env_type: sokoban
+            max_actions_per_traj: 10
+            max_tokens: 100
+        VisualSimpleSokoban:
+            env_config:
+                dim_x: 6
+                dim_y: 6
+                max_steps: 100
+                num_boxes: 1
+                render_mode: rgb_array
+            env_instruction: You are solving the Sokoban puzzle. You are the player and you need to push all boxes to targets. When you are right next to a box, you can push it by moving in the same direction. You cannot push a box through a wall, and you cannot pull a box. The answer should be a sequence of actions, like <answer>Right || Right || Up</answer>
+            env_type: sokoban
+            max_actions_per_traj: 10
+            max_tokens: 100
+        WebShop:
+            env_config:
+                dataset: small
+            env_instruction: 'You are browsing an online shop. Based on the instruction, buy a product that close to the production description. You need to search, read the search results, pick a product, choose the size and color and buy. You should only choose action from the available actions list provided later.  Example process: I need a gingko light and 20x20 pillow cover that is hand painted. First search[gingko light 20x20 pillow cover hand painted], answer format: <answer>search[blanket with fleece throw]</answer>. Valid answer is search[<keywords>] or click[<clickable>].'
+            env_type: webshop
+            max_actions_per_traj: 9
+            max_tokens: 200
+        blackjack:
+            env_config: null
+            env_instruction: |
+                You are playing Blackjack against a dealer. The dealer must hit on 16 or less and stand on 17 or more.
+                Choose either Stick or Hit. Respond with a single action.
+                Example: <answer>Hit</answer>
+            env_type: blackjack
+            max_actions_per_traj: 10
+            max_tokens: 64
+        game_2048:
+            env_config: null
+            env_instruction: |
+                You are playing the 2048 game on a 4x4 grid. Merge equal tiles by sliding Up, Right, Down, or Left.
+                If a move is invalid (no tiles move), a small penalty is applied. Respond with a single action.
+                Example: <answer>Up</answer>
+            env_type: game_2048
+            max_actions_per_traj: 700
+            max_tokens: 8192
+        rubikscube:
+            env_config:
+                max_steps: 20
+                render_mode: text
+                scramble_depth: 2
+            env_instruction: |
+                You are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.
+                Available actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.
+                - Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).
+                - Modifiers: A letter alone means 90° clockwise (e.g., 'R'). A letter with prime (') means 90° counter-clockwise (e.g., "R'").
+                Respond with a sequence of actions separated by "||".
+                Example: <answer>U</answer>
+            env_type: rubikscube
+            max_actions_per_traj: 20
+            max_tokens: 96
+custom_reward_function:
+    value:
+        name: compute_score
+        path: null
+data:
+    value:
+        custom_cls:
+            name: null
+            path: null
+        datagen:
+            name: null
+            path: null
+        dataloader_num_workers: 8
+        filter_overlong_prompts: false
+        filter_overlong_prompts_workers: 1
+        image_key: images
+        max_prompt_length: null
+        max_response_length: null
+        prompt_key: prompt
+        return_full_prompt: false
+        return_multi_modal_inputs: true
+        return_raw_chat: false
+        return_raw_input_ids: false
+        reward_fn_key: data_source
+        sampler:
+            class_name: null
+            class_path: null
+        shuffle: true
+        tokenizer: null
+        train_batch_size: 128
+        train_files: ~/data/rlhf/gsm8k/train.parquet
+        truncation: error
+        trust_remote_code: false
+        use_shm: false
+        val_batch_size: null
+        val_files: ~/data/rlhf/gsm8k/test.parquet
+        validation_shuffle: false
+        video_key: videos
+enable_response_mask:
+    value: true
+es_manager:
+    value:
+        format_penalty: -0.1
+        train:
+            env_configs:
+                n_groups:
+                    - 8
+                tags:
+                    - CoordFrozenLake
+            env_groups: 8
+            group_size: 16
+        val:
+            env_configs:
+                n_groups:
+                    - 256
+                tags:
+                    - CoordFrozenLake
+            env_groups: 256
+            group_size: 1
+global_profiler:
+    value:
+        _target_: verl.utils.profiler.ProfilerConfig
+        global_tool_config:
+            nsys:
+                _target_: verl.utils.profiler.config.NsightToolConfig
+                controller_nsight_options:
+                    cuda-graph-trace: graph
+                    cuda-memory-usage: "true"
+                    trace: cuda,nvtx,cublas,ucx
+                discrete: false
+                worker_nsight_options:
+                    capture-range: cudaProfilerApi
+                    capture-range-end: null
+                    cuda-graph-trace: graph
+                    cuda-memory-usage: "true"
+                    kill: none
+                    trace: cuda,nvtx,cublas,ucx
+            torch_memory:
+                context: all
+                stack_depth: 32
+                stacks: all
+                trace_alloc_max_entries: 100000
+        profile_continuous_steps: false
+        save_path: outputs/profile
+        steps: null
+        tool: null
+grpo_advantage_length_weight:
+    value: false
+lora:
+    value:
+        alpha: 16
+        rank: 0
+        target_modules: all-linear
+micro_batch_size_per_gpu:
+    value: 1
+model_path:
+    value: Qwen/Qwen2.5-0.5B-Instruct
+ppo_mini_batch_size:
+    value: 32
+ray_kwargs:
+    value:
+        ray_init:
+            num_cpus: null
+        timeline_json_file: null
+reward_model:
+    value:
+        enable: false
+        enable_resource_pool: false
+        forward_max_token_len_per_gpu: 32768
+        launch_reward_fn_async: false
+        max_length: null
+        micro_batch_size: null
+        micro_batch_size_per_gpu: null
+        model:
+            external_lib: null
+            fsdp_config:
+                _target_: verl.workers.config.FSDPEngineConfig
+                forward_prefetch: false
+                fsdp_size: -1
+                param_offload: false
+                reshard_after_forward: true
+                wrap_policy:
+                    min_num_params: 0
+            input_tokenizer: Qwen/Qwen2.5-0.5B-Instruct
+            path: ~/models/FsfairX-LLaMA3-RM-v0.1
+            trust_remote_code: false
+            use_fused_kernels: false
+            use_remove_padding: false
+            use_shm: false
+        n_gpus_per_node: 0
+        nnodes: 0
+        profiler:
+            _target_: verl.utils.profiler.ProfilerConfig
+            all_ranks: false
+            enable: false
+            ranks: []
+            save_path: outputs/profile
+            tool: null
+            tool_config:
+                npu:
+                    _target_: verl.utils.profiler.config.NPUToolConfig
+                    analysis: true
+                    contents: []
+                    discrete: false
+                    level: level1
+                nsys:
+                    _target_: verl.utils.profiler.config.NsightToolConfig
+                    discrete: false
+                torch:
+                    _target_: verl.utils.profiler.config.TorchProfilerToolConfig
+                    step_end: null
+                    step_start: 0
+                torch_memory:
+                    _target_: verl.utils.profiler.config.TorchMemoryToolConfig
+                    stack_depth: 32
+                    trace_alloc_max_entries: 100000
+        reward_manager: naive
+        sandbox_fusion:
+            max_concurrent: 64
+            memory_limit_mb: 1024
+            url: null
+        strategy: fsdp
+        ulysses_sequence_parallel_size: 1
+        use_dynamic_bsz: false
+seed:
+    value:
+        train: 10000
+        val: 123
+system:
+    value:
+        CUDA_VISIBLE_DEVICES: 0,1,2,3,4,5,6,7
+trainer:
+    value:
+        balance_batch: true
+        critic_warmup: 0
+        default_hdfs_dir: null
+        default_local_dir: /mnt/general/wanghy/RAGEN/saves/
+        del_local_ckpt_after_load: false
+        device: cuda
+        esi_redundant_time: 0
+        experiment_name: frozenlake-static-starpos-stateestimate
+        generations_to_log_to_wandb:
+            train: 128
+            val: 20
+        local_log_dir: results/
+        log_val_generations: 0
+        logger:
+            - console
+            - wandb
+        max_actor_ckpt_to_keep: 1
+        max_critic_ckpt_to_keep: 1
+        n_gpus_per_node: 8
+        nnodes: 1
+        project_name: ragen_latest_qwen_05B_it
+        ray_wait_register_center_timeout: 300
+        resume_from_path: null
+        resume_mode: auto
+        rollout_data_dir: null
+        save_freq: -1
+        test_freq: 10
+        total_epochs: 30
+        total_training_steps: 200
+        use_legacy_worker_impl: auto
+        val_before_train: true
+        val_only: false
+        validation_data_dir: null
+        validation_steps: 1

wandb/run-20251218_002911-rvpar64n/files/requirements.txt

@@ -0,0 +1,316 @@
+ragen==0.1
+ragen==0.1
+colorama==0.4.6
+psutil==7.1.2
+ragen==0.1
+setuptools==80.9.0
+wheel==0.45.1
+pip==25.3
+ragen==0.1
+pytz==2025.2
+nvidia-cusparselt-cu12==0.6.2
+mpmath==1.3.0
+typing_extensions==4.15.0
+sympy==1.13.1
+pylatexenc==2.10
+nvidia-cusolver-cu12==11.6.1.9
+numpy==1.26.4
+Markdown==3.10
+absl-py==2.3.1
+pyasn1_modules==0.4.2
+Werkzeug==3.1.3
+networkx==3.3
+MarkupSafe==2.1.5
+fsspec==2025.9.0
+filelock==3.19.1
+nvidia-cudnn-cu12==9.1.0.70
+Jinja2==3.1.6
+tensorboard==2.20.0
+triton==3.2.0
+pillow==11.3.0
+xxhash==3.6.0
+nvidia-nvtx-cu12==12.4.127
+nvidia-nvjitlink-cu12==12.4.127
+nvidia-nccl-cu12==2.21.5
+nvidia-curand-cu12==10.3.5.147
+wrapt==2.0.1
+nvidia-cufft-cu12==11.2.1.3
+pyjnius==1.7.0
+nvidia-cuda-runtime-cu12==12.4.127
+nvidia-cuda-nvrtc-cu12==12.4.127
+websockets==15.0.1
+nvidia-cuda-cupti-cu12==12.4.127
+zipp==3.23.0
+nvidia-cublas-cu12==12.4.5.8
+nvidia-cusparse-cu12==12.3.1.170
+flash_attn==2.8.3
+rsa==4.9.1
+einops==0.8.1
+py-cpuinfo==9.0.0
+pure_eval==0.2.3
+ptyprocess==0.7.0
+gym-notices==0.1.0
+flatbuffers==25.9.23
+fastrlock==0.8.3
+Farama-Notifications==0.0.4
+faiss-gpu==1.7.2
+antlr4-python3-runtime==4.9.3
+wcwidth==0.2.14
+wasabi==1.1.3
+uvloop==0.22.1
+urllib3==2.5.0
+tzdata==2025.2
+typing-inspection==0.4.2
+traitlets==5.14.3
+tqdm==4.67.1
+tomli==2.3.0
+threadpoolctl==3.6.0
+tenacity==9.1.2
+tabulate==0.9.0
+spacy-loggers==1.0.5
+spacy-legacy==3.0.12
+soupsieve==2.8
+sniffio==1.3.1
+smmap==5.0.2
+six==1.17.0
+shellingham==1.5.4
+sentencepiece==0.2.1
+scipy==1.15.3
+safetensors==0.6.2
+rpds-py==0.29.0
+rignore==0.7.6
+regex==2025.11.3
+RapidFuzz==3.14.3
+rank-bm25==0.2.2
+pyzmq==27.1.0
+PyYAML==6.0.3
+pytokens==0.3.0
+python-multipart==0.0.20
+python-json-logger==4.0.0
+python-dotenv==1.2.1
+PySocks==1.7.1
+pyparsing==3.2.5
+PyJWT==2.10.1
+Pygments==2.19.2
+pygame==2.6.1
+pydantic_core==2.41.5
+pycparser==2.23
+pycountry==24.6.1
+pybind11==3.0.1
+pyarrow==22.0.0
+psutil==7.1.3
+protobuf==4.25.8
+propcache==0.4.1
+prometheus_client==0.23.1
+platformdirs==4.5.0
+pexpect==4.9.0
+pathspec==0.12.1
+partial-json-parser==0.2.1.1.post6
+parso==0.8.5
+packaging==25.0
+orjson==3.11.4
+opentelemetry-semantic-conventions-ai==0.4.13
+opencv-python-headless==4.12.0.88
+ninja==1.13.0
+nest-asyncio==1.6.0
+mypy_extensions==1.1.0
+murmurhash==1.0.15
+multidict==6.7.0
+msgspec==0.19.0
+msgpack==1.1.2
+mdurl==0.1.2
+loguru==0.7.3
+llvmlite==0.44.0
+llguidance==0.7.30
+lark==1.2.2
+kiwisolver==1.4.9
+joblib==1.5.2
+jiter==0.12.0
+itsdangerous==2.2.0
+interegular==0.3.3
+ImageIO==2.37.2
+idna==3.11
+humanfriendly==10.0
+httpx-sse==0.4.3
+httptools==0.7.1
+html2text==2025.4.15
+hf-xet==1.2.0
+h11==0.16.0
+grpcio==1.76.0
+frozenlist==1.8.0
+fonttools==4.60.1
+executing==2.2.1
+exceptiongroup==1.3.0
+eval_type_backport==0.2.2
+docstring_parser==0.17.0
+dnspython==2.8.0
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The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 0/20\n\nUp (U):    [W, Y]\n [W, Y]\nLeft (L):  [O, O]\n [G, B]\nFront (F): [G, B]\n [O, O]\nRight (R): [R, R]\n [G, B]\nBack (B):  [G, B]\n [R, R]\nDown (D):  [Y, Y]\n [W, W]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 20 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, the Down face has two white stickers that should be on the Up face. By rotating the Down face counter-clockwise (D'), I can align one of these white stickers with the Up face, which is a step towards solving the cube.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 1/20\n\nUp (U):    [W, Y]\n [W, Y]\nLeft (L):  [O, O]\n [O, O]\nFront (F): [G, B]\n [G, B]\nRight (R): [R, R]\n [R, R]\nBack (B):  [G, B]\n [G, B]\nDown (D):  [Y, W]\n [Y, W]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 19 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the right side (R) is showing red, which is not in its solved position. By applying the action R', I aim to move the white and green pieces from the up and front faces to the right face, potentially aligning colors closer to their solved positions.</think><answer>R'</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 2/20\n\nUp (U):    [W, G]\n [W, G]\nLeft (L):  [O, O]\n [O, O]\nFront (F): [G, Y]\n [G, Y]\nRight (R): [R, R]\n [R, R]\nBack (B):  [W, B]\n [W, B]\nDown (D):  [Y, B]\n [Y, B]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 18 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the right side (R) is showing red (R), which is not in its solved position. To progress towards solving the cube, I need to move the correct color to the right side. Since the correct color for the right side is red and it's already on the right side but not in the correct position, I should rotate the right side counterclockwise to align the red color correctly. Therefore, my next action is R'.</think><answer>R'</answer>\n", 1.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 0/20\n\nUp (U):    [B, G]\n [B, G]\nLeft (L):  [O, O]\n [W, Y]\nFront (F): [W, Y]\n [O, O]\nRight (R): [R, R]\n [W, Y]\nBack (B):  [W, Y]\n [R, R]\nDown (D):  [G, G]\n [B, B]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 20 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, the Down face has two colors that should not be there: Green and Blue. By rotating the Down face counter-clockwise (D'), I can move these misplaced colors to the Up and Right faces, respectively, where they can be more easily manipulated in subsequent moves.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 1/20\n\nUp (U):    [B, G]\n [B, G]\nLeft (L):  [O, O]\n [O, O]\nFront (F): [W, Y]\n [W, Y]\nRight (R): [R, R]\n [R, R]\nBack (B):  [W, Y]\n [W, Y]\nDown (D):  [G, B]\n [G, B]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 19 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the cube, the right side (R) is showing red, which is not in its solved position. By applying the R' action, I can rotate the right side counterclockwise, aiming to align the colors correctly. This move is chosen based on the visible need to correct the misalignment of the red color on the right side.</think><answer>R'</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 2/20\n\nUp (U):    [B, W]\n [B, W]\nLeft (L):  [O, O]\n [O, O]\nFront (F): [W, G]\n [W, G]\nRight (R): [R, R]\n [R, R]\nBack (B):  [B, Y]\n [B, Y]\nDown (D):  [G, Y]\n [G, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 18 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the left face (L) is showing two orange colors, which are correct but in the wrong position. To move these colors into a more correct position without disrupting the other faces, I should rotate the left face clockwise (L'). This action will align the orange colors on the left face with the orange center piece, which is a step towards solving the cube.</think><answer>L'</answer>\n", 1.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 0/20\n\nUp (U):    [W, W]\n [W, W]\nLeft (L):  [O, O]\n [B, B]\nFront (F): [G, G]\n [O, O]\nRight (R): [R, R]\n [G, G]\nBack (B):  [B, B]\n [R, R]\nDown (D):  [Y, Y]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 20 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the cube, the Down face is already correctly aligned with yellow (Y) on top. To progress, I need to align the other colors on their respective sides. Rotating the Down face counter-clockwise (D') will bring the misaligned green (G) and orange (O) pieces to the Front and Left faces, respectively, where they can be moved into their correct positions in subsequent moves.</think><answer>D'</answer>\n", 1.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 15/20\n\nUp (U):    [O, W]\n [R, B]\nLeft (L):  [B, B]\n [R, G]\nFront (F): [W, R]\n [Y, B]\nRight (R): [Y, G]\n [O, G]\nBack (B):  [R, W]\n [O, G]\nDown (D):  [O, Y]\n [Y, W]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 5 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, the Down face has two different colors, O and Y, which are not aligned with their respective faces. By applying D', I aim to move the O piece to the Left face and the Y piece to the Back face, potentially aligning them with their correct colors.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 16/20\n\nUp (U):    [O, W]\n [R, B]\nLeft (L):  [B, B]\n [Y, B]\nFront (F): [W, R]\n [O, G]\nRight (R): [Y, G]\n [O, G]\nBack (B):  [R, W]\n [R, G]\nDown (D):  [Y, W]\n [O, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 4 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, moving the left side (L) will help align the blue and yellow colors on the left side, which are currently disoriented. This move is intended to progress towards a state where each side of the cube has a uniform color.</think><answer>L</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 17/20\n\nUp (U):    [G, W]\n [W, B]\nLeft (L):  [Y, B]\n [B, B]\nFront (F): [O, R]\n [R, G]\nRight (R): [Y, G]\n [O, G]\nBack (B):  [R, O]\n [R, Y]\nDown (D):  [W, W]\n [O, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 3 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, the bottom face has a white and an orange tile that need to be aligned with their respective faces. By applying D', I can move the out-of-place orange tile to the front face, which is closer to its correct position.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 4:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 18/20\n\nUp (U):    [G, W]\n [W, B]\nLeft (L):  [Y, B]\n [R, G]\nFront (F): [O, R]\n [O, G]\nRight (R): [Y, G]\n [R, Y]\nBack (B):  [R, O]\n [B, B]\nDown (D):  [W, Y]\n [W, O]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 2 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, moving the Down face clockwise (D) would not align any of the colors on the cube, whereas moving the Down face counterclockwise (D') will align the white and orange pieces on the Down face with their respective colors on the Front and Left faces.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 5:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 19/20\n\nUp (U):    [G, W]\n [W, B]\nLeft (L):  [Y, B]\n [O, G]\nFront (F): [O, R]\n [R, Y]\nRight (R): [Y, G]\n [B, B]\nBack (B):  [R, O]\n [R, G]\nDown (D):  [Y, O]\n [W, W]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 1 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, applying D' will move the yellow piece from the bottom face to the front face, aligning it with the yellow center piece on the left face, which is a step towards solving the cube.</think><answer>D'</answer>\n", 0.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 0/20\n\nUp (U):    [B, B]\n [B, B]\nLeft (L):  [W, W]\n [O, O]\nFront (F): [R, R]\n [W, W]\nRight (R): [Y, Y]\n [R, R]\nBack (B):  [O, O]\n [Y, Y]\nDown (D):  [G, G]\n [G, G]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 20 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the cube, the Down face is already uniform in green, but to progress, I need to consider the effect of my moves on the rest of the cube. Moving the Down face counter-clockwise (D') will bring the out-of-place white and red tiles on the Front face to the Down face, potentially setting up a better position for future moves to align colors.</think><answer>D'</answer>\n", 1.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 0/20\n\nUp (U):    [W, B]\n [G, Y]\nLeft (L):  [O, R]\n [O, R]\nFront (F): [W, G]\n [W, G]\nRight (R): [O, R]\n [O, R]\nBack (B):  [Y, B]\n [Y, B]\nDown (D):  [B, W]\n [Y, G]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 20 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, the front face has a white piece in the bottom left that should be on the up face. Rotating the front face clockwise (F) will move this piece to the left face, where it can be more easily manipulated into its correct position.</think><answer>F</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 1/20\n\nUp (U):    [W, B]\n [R, R]\nLeft (L):  [O, B]\n [O, W]\nFront (F): [W, W]\n [G, G]\nRight (R): [G, R]\n [Y, R]\nBack (B):  [Y, B]\n [Y, B]\nDown (D):  [O, O]\n [Y, G]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 19 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, the front face has white and green, which is not in the correct position. By applying the F action, I can move the white pieces on the front face to the up face where they belong, aligning with the white center piece.</think><answer>F</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 2/20\n\nUp (U):    [W, B]\n [W, B]\nLeft (L):  [O, O]\n [O, O]\nFront (F): [G, W]\n [G, W]\nRight (R): [R, R]\n [R, R]\nBack (B):  [Y, B]\n [Y, B]\nDown (D):  [Y, G]\n [Y, G]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 18 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the front face has a green and a white tile, which are not in their correct positions. By applying the 'R' action, I can move the white tile on the right face to the front face, potentially aligning it with the white center tile on the up face. This move could simplify future steps in solving the cube.</think><answer>R</answer>\n", 1.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 15/20\n\nUp (U):    [G, W]\n [Y, W]\nLeft (L):  [R, Y]\n [R, G]\nFront (F): [W, G]\n [O, B]\nRight (R): [R, B]\n [O, W]\nBack (B):  [O, Y]\n [B, Y]\nDown (D):  [G, O]\n [B, R]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 5 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, I notice that the left side (L) has a mixed color configuration. By applying the L action, I can move the green piece from the front (F) to the left (L) side, aligning it with the green on the top (U) and potentially setting up a better configuration for solving the cube.</think><answer>L</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 16/20\n\nUp (U):    [Y, W]\n [Y, W]\nLeft (L):  [R, R]\n [G, Y]\nFront (F): [G, G]\n [Y, B]\nRight (R): [R, B]\n [O, W]\nBack (B):  [O, B]\n [B, G]\nDown (D):  [W, O]\n [O, R]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 4 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, applying D' (down face counter-clockwise) will move the white and orange pieces from the bottom face to the front and right faces, respectively, potentially setting up a more favorable position for solving the cube.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 17/20\n\nUp (U):    [Y, W]\n [Y, W]\nLeft (L):  [R, R]\n [Y, B]\nFront (F): [G, G]\n [O, W]\nRight (R): [R, B]\n [B, G]\nBack (B):  [O, B]\n [G, Y]\nDown (D):  [O, R]\n [W, O]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 3 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, the Down face has two different colors, O and R, which are not aligned with their respective sides. By applying D', I aim to move the O piece to the Left side where it should be, and the R piece to the Front side, aligning them correctly with their respective colors.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 4:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 18/20\n\nUp (U):    [Y, W]\n [Y, W]\nLeft (L):  [R, R]\n [O, W]\nFront (F): [G, G]\n [B, G]\nRight (R): [R, B]\n [G, Y]\nBack (B):  [O, B]\n [Y, B]\nDown (D):  [R, O]\n [O, W]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 2 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the front face has two green tiles on the bottom that need to be aligned with the green center. Rotating the front face counter-clockwise (F') will move these tiles up, aligning them correctly with the green center.</think><answer>F'</answer>\nuser\nReward:\n0.0\n\nTurn 5:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 19/20\n\nUp (U):    [Y, W]\n [R, G]\nLeft (L):  [R, W]\n [O, Y]\nFront (F): [G, G]\n [G, B]\nRight (R): [O, B]\n [R, Y]\nBack (B):  [O, B]\n [Y, B]\nDown (D):  [R, W]\n [O, W]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 1 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the front face has two green tiles on top that need to be aligned with the green center. By applying the 'F' action, I can rotate the front face clockwise, which will move the green tiles from the top row of the front face to their correct positions on the left and right sides of the front face, aligning them with the green center.</think><answer>F</answer>\n", 0.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 0/20\n\nUp (U):    [W, W]\n [W, W]\nLeft (L):  [O, O]\n [G, G]\nFront (F): [G, G]\n [R, R]\nRight (R): [R, R]\n [B, B]\nBack (B):  [B, B]\n [O, O]\nDown (D):  [Y, Y]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 20 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the cube, the Down face is already uniform in color, which is yellow. However, the other faces are not yet solved. To progress, I need to start aligning the colors on the other faces while keeping the yellow face intact. The simplest and most direct action to begin this alignment is to rotate the Down face, which will not disturb its uniform color but will allow me to see how the other colors align with their respective faces. Therefore, I will rotate the Down face clockwise.</think><answer>D</answer>\n", 1.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 15/20\n\nUp (U):    [G, W]\n [B, Y]\nLeft (L):  [R, W]\n [R, W]\nFront (F): [R, G]\n [O, B]\nRight (R): [O, O]\n [Y, Y]\nBack (B):  [G, Y]\n [B, W]\nDown (D):  [B, R]\n [G, O]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 5 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, applying the L action will rotate the left face clockwise, which seems like a good move to start aligning colors. I'll rotate the left face to see if I can get any of the colors to match on the adjacent faces.</think><answer>L</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 16/20\n\nUp (U):    [W, W]\n [Y, Y]\nLeft (L):  [R, R]\n [W, W]\nFront (F): [G, G]\n [B, B]\nRight (R): [O, O]\n [Y, Y]\nBack (B):  [G, G]\n [B, B]\nDown (D):  [R, R]\n [O, O]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 4 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, I notice that the left side (L) has the correct colors at the top but is out of place. By applying the L' action, I can move the white (W) from the top (U) to the left (L) side where it belongs, while also moving the red (R) from the left (L) side to the front (F) side, which is also a step towards solving the cube.</think><answer>L'</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 17/20\n\nUp (U):    [G, W]\n [B, Y]\nLeft (L):  [R, W]\n [R, W]\nFront (F): [R, G]\n [O, B]\nRight (R): [O, O]\n [Y, Y]\nBack (B):  [G, Y]\n [B, W]\nDown (D):  [B, R]\n [G, O]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 3 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the left side has two white pieces on the bottom that should be on the up side. By applying the L' action, I can move these white pieces to the up side, aligning them correctly with the white center piece.</think><answer>L'</answer>\nuser\nReward:\n0.0\n\nTurn 4:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 18/20\n\nUp (U):    [R, W]\n [O, Y]\nLeft (L):  [W, W]\n [R, R]\nFront (F): [B, G]\n [G, B]\nRight (R): [O, O]\n [Y, Y]\nBack (B):  [G, B]\n [B, G]\nDown (D):  [W, R]\n [Y, O]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 2 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, I notice that the left face has two white pieces on the bottom, which are out of place. By applying the L action, I can move these pieces to the top of the left face, potentially aligning them with the white center piece on the up face. This move could simplify the cube's state, bringing it closer to a solved configuration.</think><answer>L</answer>\nuser\nReward:\n0.0\n\nTurn 5:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 19/20\n\nUp (U):    [G, W]\n [B, Y]\nLeft (L):  [R, W]\n [R, W]\nFront (F): [R, G]\n [O, B]\nRight (R): [O, O]\n [Y, Y]\nBack (B):  [G, Y]\n [B, W]\nDown (D):  [B, R]\n [G, O]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 1 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, the left face has two white stickers that should be on the up face. By applying the L action, I can move these stickers to the up face, aligning them closer to their correct positions.</think><answer>L</answer>\n", 0.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 2/20\n\nUp (U):    [O, B]\n [O, B]\nLeft (L):  [Y, Y]\n [W, W]\nFront (F): [G, O]\n [R, B]\nRight (R): [W, W]\n [Y, Y]\nBack (B):  [R, B]\n [G, O]\nDown (D):  [G, R]\n [G, R]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 18 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the bottom face has two green tiles and two red tiles. By applying the D' action, I can move the green tiles from the bottom face to the front and back faces, potentially aligning them with their respective colors on the top face.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 3/20\n\nUp (U):    [O, B]\n [O, B]\nLeft (L):  [Y, Y]\n [R, B]\nFront (F): [G, O]\n [Y, Y]\nRight (R): [W, W]\n [G, O]\nBack (B):  [R, B]\n [W, W]\nDown (D):  [R, R]\n [G, G]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 17 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, moving the Down face clockwise (D) would not align any of the colors, but moving it counterclockwise (D') would align the green and orange on the front and left faces, respectively. This action is chosen to progress towards solving the cube by aligning colors on the faces.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 4/20\n\nUp (U):    [O, B]\n [O, B]\nLeft (L):  [Y, Y]\n [Y, Y]\nFront (F): [G, O]\n [G, O]\nRight (R): [W, W]\n [W, W]\nBack (B):  [R, B]\n [R, B]\nDown (D):  [R, G]\n [R, G]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 16 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the right side (R) has white (W) on top which should align with the top (U) side's color. To move the white on the right side to the top, I need to rotate the right side counterclockwise. Therefore, the action R' is appropriate to align the white with the top side.</think><answer>R'</answer>\nuser\nReward:\n0.0\n\nTurn 4:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 5/20\n\nUp (U):    [O, R]\n [O, R]\nLeft (L):  [Y, Y]\n [Y, Y]\nFront (F): [G, B]\n [G, B]\nRight (R): [W, W]\n [W, W]\nBack (B):  [G, B]\n [G, B]\nDown (D):  [R, O]\n [R, O]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 15 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the right side (R) has white (W) on top, which is not in its solved position. To move the white pieces to the top face (U) where they belong, I need to rotate the right side counter-clockwise (R'). This will align the white pieces on the right side with the white center piece on the top face.</think><answer>R'</answer>\nuser\nReward:\n0.0\n\nTurn 5:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 6/20\n\nUp (U):    [O, G]\n [O, G]\nLeft (L):  [Y, Y]\n [Y, Y]\nFront (F): [G, R]\n [G, R]\nRight (R): [W, W]\n [W, W]\nBack (B):  [O, B]\n [O, B]\nDown (D):  [R, B]\n [R, B]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 14 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the right face (R) has white (W) on top which should be aligned with the white center on the up face (U). To achieve this, I need to rotate the right face counterclockwise (R') to align the white pieces with the white center.</think><answer>R'</answer>\n", 1.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 0/20\n\nUp (U):    [R, G]\n [B, W]\nLeft (L):  [W, O]\n [B, Y]\nFront (F): [W, G]\n [O, O]\nRight (R): [R, Y]\n [W, Y]\nBack (B):  [R, B]\n [R, Y]\nDown (D):  [G, G]\n [B, O]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 20 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the cube, the back face has a misaligned color 'B' that should be on the left face. Rotating the back face counter-clockwise (B') will move the 'B' color to the left face, aligning it with the correct color.</think><answer>B'</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 1/20\n\nUp (U):    [B, W]\n [B, W]\nLeft (L):  [O, O]\n [B, Y]\nFront (F): [W, G]\n [O, O]\nRight (R): [R, R]\n [W, G]\nBack (B):  [B, Y]\n [R, R]\nDown (D):  [G, G]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 19 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, applying D' (down face counter-clockwise) seems like a good move to start aligning the colors. This action will move the green and yellow pieces from the down face to the front and right faces, respectively, potentially setting up for more efficient moves in the future.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 2/20\n\nUp (U):    [B, W]\n [B, W]\nLeft (L):  [O, O]\n [O, O]\nFront (F): [W, G]\n [W, G]\nRight (R): [R, R]\n [R, R]\nBack (B):  [B, Y]\n [B, Y]\nDown (D):  [G, Y]\n [G, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 18 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the left side (L) is entirely orange, which is correct, but the front side (F) has a white piece that should be on the up side (U). To move this white piece to the up side, I need to rotate the left side clockwise (L'), which will bring the white piece to the up side.</think><answer>L'</answer>\n", 1.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 15/20\n\nUp (U):    [W, W]\n [W, W]\nLeft (L):  [O, O]\n [O, O]\nFront (F): [G, R]\n [G, G]\nRight (R): [R, R]\n [R, G]\nBack (B):  [B, B]\n [B, B]\nDown (D):  [Y, Y]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 5 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the front face has a green and red tile that needs to be aligned correctly. By applying the D' action, I can move the misaligned green tile on the right face to the front face, positioning it to be aligned with the green center tile on the front face in future moves.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 16/20\n\nUp (U):    [W, W]\n [W, W]\nLeft (L):  [O, O]\n [G, G]\nFront (F): [G, R]\n [R, G]\nRight (R): [R, R]\n [B, B]\nBack (B):  [B, B]\n [O, O]\nDown (D):  [Y, Y]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 4 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the Down (D) face is already uniform in yellow (Y). To progress, I should look to align the colors on the adjacent faces. The D' action will bring the misaligned green (G) and red (R) from the Front (F) and Right (R) faces to the Down (D) face, potentially setting up for future moves to align these colors correctly.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 17/20\n\nUp (U):    [W, W]\n [W, W]\nLeft (L):  [O, O]\n [R, G]\nFront (F): [G, R]\n [B, B]\nRight (R): [R, R]\n [O, O]\nBack (B):  [B, B]\n [G, G]\nDown (D):  [Y, Y]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 3 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, my goal is to move the cube towards a solved state. The Down (D) face is already uniform in yellow (Y), but to align the other colors correctly, I need to move the yellow center piece to the correct position. The action D' (Down face, counter-clockwise) will move the yellow center piece to the front, allowing for further alignment of the cube's colors.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 4:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 18/20\n\nUp (U):    [W, W]\n [W, W]\nLeft (L):  [O, O]\n [B, B]\nFront (F): [G, R]\n [O, O]\nRight (R): [R, R]\n [G, G]\nBack (B):  [B, B]\n [R, G]\nDown (D):  [Y, Y]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 2 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the Down face is already uniform in yellow, indicating that the bottom layer might be solved or close to being solved. To continue solving the cube, I should look to align the edge pieces correctly. Since the Down face is correct, I need to check the pieces around it. The D' action will move the bottom layer clockwise, potentially aligning the edge pieces correctly for the next steps in solving the cube.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 5:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 19/20\n\nUp (U):    [W, W]\n [W, W]\nLeft (L):  [O, O]\n [O, O]\nFront (F): [G, R]\n [G, G]\nRight (R): [R, R]\n [R, G]\nBack (B):  [B, B]\n [B, B]\nDown (D):  [Y, Y]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 1 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the front face has a green tile out of place, which should be on the left face. To move this tile to its correct position, I need to rotate the back face clockwise, which will bring the green tile to the left face. However, the action required is the opposite, a counter-clockwise rotation of the back face, denoted as B'. This action will correctly position the green tile on the left face.</think><answer>B'</answer>\n", 0.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 0/20\n\nUp (U):    [O, W]\n [O, R]\nLeft (L):  [W, W]\n [B, O]\nFront (F): [B, G]\n [Y, G]\nRight (R): [Y, G]\n [Y, R]\nBack (B):  [R, G]\n [B, W]\nDown (D):  [B, O]\n [R, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 20 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, the left face has two white pieces that should be on the up face. By rotating the left face clockwise (L), I can move these white pieces closer to their correct position on the up face.</think><answer>L</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 1/20\n\nUp (U):    [W, W]\n [G, R]\nLeft (L):  [B, W]\n [O, W]\nFront (F): [O, G]\n [O, G]\nRight (R): [Y, G]\n [Y, R]\nBack (B):  [R, R]\n [B, B]\nDown (D):  [B, O]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 19 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, I notice that the front face has two different colors, O and G. By applying the F action, I can move the O color from the front face to the left face, which currently has the same O color, potentially aligning colors on the cube's faces.</think><answer>F</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 2/20\n\nUp (U):    [W, W]\n [W, W]\nLeft (L):  [B, B]\n [O, O]\nFront (F): [O, O]\n [G, G]\nRight (R): [G, G]\n [R, R]\nBack (B):  [R, R]\n [B, B]\nDown (D):  [Y, Y]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 18 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the top (Up) face is already uniform in white color. However, the cube is not fully solved as other faces show mixed colors. To progress towards solving the cube, I should start by rotating the top face to see if this action aligns the colors on the adjacent faces better. Thus, rotating the top face clockwise (U) is my next move.</think><answer>U</answer>\n", 1.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 15/20\n\nUp (U):    [W, O]\n [Y, W]\nLeft (L):  [R, G]\n [O, G]\nFront (F): [O, B]\n [R, R]\nRight (R): [O, B]\n [B, R]\nBack (B):  [Y, G]\n [W, G]\nDown (D):  [Y, Y]\n [W, B]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 5 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, applying D' will rotate the bottom face counterclockwise, which seems like a good move to progress towards solving the cube. This action is chosen based on the current configuration of the cube and the goal of aligning colors on each face.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 16/20\n\nUp (U):    [W, O]\n [Y, W]\nLeft (L):  [R, G]\n [R, R]\nFront (F): [O, B]\n [B, R]\nRight (R): [O, B]\n [W, G]\nBack (B):  [Y, G]\n [O, G]\nDown (D):  [Y, B]\n [Y, W]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 4 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, I need to align the colors on each face. The Down face has two yellow pieces that should be on the Up face, and the Down face also has a blue piece that should be on the Front face. To move the yellow pieces up and the blue piece to the Front, I should perform the inverse of the Down move, which is D'. This will bring the yellow pieces closer to their correct position on the Up face.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 17/20\n\nUp (U):    [W, O]\n [Y, W]\nLeft (L):  [R, G]\n [B, R]\nFront (F): [O, B]\n [W, G]\nRight (R): [O, B]\n [O, G]\nBack (B):  [Y, G]\n [R, R]\nDown (D):  [B, W]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 3 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, I notice that the bottom layer has a scrambled configuration. By applying the D' action, I aim to position the yellow pieces correctly on the Down face without disrupting the other faces that are closer to being solved. This move is selected based on the visible need to align the yellow pieces on the D face.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 4:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 18/20\n\nUp (U):    [W, O]\n [Y, W]\nLeft (L):  [R, G]\n [W, G]\nFront (F): [O, B]\n [O, G]\nRight (R): [O, B]\n [R, R]\nBack (B):  [Y, G]\n [B, R]\nDown (D):  [W, Y]\n [B, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 2 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the Down face has two yellow pieces that should be on the Up face. By rotating the Down face counter-clockwise (D'), I can move these yellow pieces closer to their correct position on the Up face.</think><answer>D'</answer>\nuser\nReward:\n0.0\n\nTurn 5:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 19/20\n\nUp (U):    [W, O]\n [Y, W]\nLeft (L):  [R, G]\n [O, G]\nFront (F): [O, B]\n [R, R]\nRight (R): [O, B]\n [B, R]\nBack (B):  [Y, G]\n [W, G]\nDown (D):  [Y, Y]\n [W, B]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 1 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the Down (D) face has two yellow pieces on it, which are out of place. By applying the D' action, I can move these yellow pieces to the Up (U) face, which is a step towards solving the cube.</think><answer>D'</answer>\n", 0.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 0/20\n\nUp (U):    [W, R]\n [W, B]\nLeft (L):  [O, O]\n [Y, R]\nFront (F): [G, W]\n [B, B]\nRight (R): [R, G]\n [O, W]\nBack (B):  [Y, B]\n [R, G]\nDown (D):  [Y, Y]\n [O, G]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 20 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the cube, the bottom face has colors that should be on other faces. Rotating the bottom face clockwise (D) will bring a yellow piece to the front and a green piece to the left, which are closer to their correct positions.</think><answer>D</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 1/20\n\nUp (U):    [W, R]\n [W, B]\nLeft (L):  [O, O]\n [R, G]\nFront (F): [G, W]\n [Y, R]\nRight (R): [R, G]\n [B, B]\nBack (B):  [Y, B]\n [O, W]\nDown (D):  [O, Y]\n [G, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 19 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the upper face has two white pieces that need to be aligned with the white center. Rotating the upper face clockwise (U) will align one of the white pieces with the white center, which is a step towards solving the cube.</think><answer>U</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 2/20\n\nUp (U):    [W, W]\n [B, R]\nLeft (L):  [G, W]\n [R, G]\nFront (F): [R, G]\n [Y, R]\nRight (R): [Y, B]\n [B, B]\nBack (B):  [O, O]\n [O, W]\nDown (D):  [O, Y]\n [G, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 18 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, the Down face has two colors that don't match the center, which suggests that the cube is not solved. By applying the D action, I aim to move the yellow piece from the Down face to the Front face, potentially aligning it with the yellow center. This could simplify the cube's state, making it easier to solve in subsequent turns.</think><answer>D</answer>\nuser\nReward:\n0.0\n\nTurn 4:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 3/20\n\nUp (U):    [W, W]\n [B, R]\nLeft (L):  [G, W]\n [O, W]\nFront (F): [R, G]\n [R, G]\nRight (R): [Y, B]\n [Y, R]\nBack (B):  [O, O]\n [B, B]\nDown (D):  [G, O]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 17 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the front face has two different colors, R and G. By applying the F action, I can move the uniform colors on the left and right faces to the front, aligning the R colors together and potentially setting up a more uniform face for future moves.</think><answer>F</answer>\nuser\nReward:\n0.0\n\nTurn 5:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 4/20\n\nUp (U):    [W, W]\n [W, W]\nLeft (L):  [G, G]\n [O, O]\nFront (F): [R, R]\n [G, G]\nRight (R): [B, B]\n [R, R]\nBack (B):  [O, O]\n [B, B]\nDown (D):  [Y, Y]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 16 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the Down (D) face is already correctly aligned with yellow (Y) on top. To continue solving the cube, I need to look for a move that will align another color on its respective face. The Front (F) face has green (G) which should be on the Left (L) face. To move the green piece on the Front face to the Left face, I need to rotate the bottom layer in a way that brings the green piece to the bottom, then use a move to position it correctly. A D' move will bring the green piece from the front to the bottom, setting up for the next steps in solving the cube.</think><answer>D'</answer>\n", 1.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 15/20\n\nUp (U):    [Y, R]\n [Y, Y]\nLeft (L):  [B, R]\n [Y, R]\nFront (F): [G, G]\n [R, G]\nRight (R): [O, B]\n [O, O]\nBack (B):  [W, O]\n [B, B]\nDown (D):  [W, W]\n [G, W]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 5 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, I notice that the front face has two green tiles on top and a red tile on the bottom. By applying the action F', I can rotate the front face clockwise, which will move the red tile from the front face to the down face, potentially aligning it better for future moves or solving the cube.</think><answer>F'</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 16/20\n\nUp (U):    [Y, R]\n [O, O]\nLeft (L):  [B, Y]\n [Y, Y]\nFront (F): [G, G]\n [G, R]\nRight (R): [W, B]\n [W, O]\nBack (B):  [W, O]\n [B, B]\nDown (D):  [R, R]\n [G, W]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 4 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the left face has two yellow pieces on the bottom that need to be aligned with the yellow center on the up face. By executing an L action, I can move these yellow pieces to the top of the left face, aligning them correctly with the yellow center.</think><answer>L</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 17/20\n\nUp (U):    [B, R]\n [O, O]\nLeft (L):  [Y, B]\n [Y, Y]\nFront (F): [Y, G]\n [O, R]\nRight (R): [W, B]\n [W, O]\nBack (B):  [W, G]\n [B, R]\nDown (D):  [G, R]\n [G, W]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 3 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the left face has two yellow pieces on top, which are out of place. By applying the L action, I can move these yellow pieces to the front face, potentially aligning them closer to their correct positions on the yellow (Up) face.</think><answer>L</answer>\nuser\nReward:\n0.0\n\nTurn 4:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 18/20\n\nUp (U):    [R, R]\n [G, O]\nLeft (L):  [Y, Y]\n [Y, B]\nFront (F): [B, G]\n [O, R]\nRight (R): [W, B]\n [W, O]\nBack (B):  [W, G]\n [B, G]\nDown (D):  [Y, R]\n [O, W]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 2 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, the right side (R) has a white (W) and an orange (O) that should be aligned with the up (U) and front (F) respectively. Rotating the right side counter-clockwise (R') will align the W with the U and O with the F, moving towards solving the cube.</think><answer>R'</answer>\nuser\nReward:\n0.0\n\nTurn 5:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 19/20\n\nUp (U):    [R, B]\n [G, W]\nLeft (L):  [Y, Y]\n [Y, B]\nFront (F): [B, R]\n [O, O]\nRight (R): [B, O]\n [W, W]\nBack (B):  [W, G]\n [R, G]\nDown (D):  [Y, G]\n [O, R]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 1 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state, applying L' will move the white and green pieces from the left side to the top, aligning them with the white center and setting up a potential for future moves to solve the cube.</think><answer>L'</answer>\n", 0.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 0/20\n\nUp (U):    [W, W]\n [W, W]\nLeft (L):  [B, B]\n [R, R]\nFront (F): [O, O]\n [B, B]\nRight (R): [G, G]\n [O, O]\nBack (B):  [R, R]\n [G, G]\nDown (D):  [Y, Y]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 20 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the cube, the Down face is already correctly aligned with yellow (Y) on top. However, the other faces are not yet in their correct configurations. By rotating the Down face counter-clockwise (D'), I can position the misaligned colors on the sides to be moved into their correct faces in subsequent turns.</think><answer>D'</answer>\n", 1.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 0/20\n\nUp (U):    [W, W]\n [O, O]\nLeft (L):  [O, Y]\n [O, Y]\nFront (F): [G, G]\n [G, G]\nRight (R): [W, R]\n [W, R]\nBack (B):  [B, B]\n [B, B]\nDown (D):  [R, R]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 20 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the cube, the front face has two green tiles that need to be aligned with the rest of the green face. Rotating the front face counter-clockwise (F') will align the green tiles on the front face with the green center, making progress towards the goal of having each face a single color.</think><answer>F'</answer>\n", 1.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 0/20\n\nUp (U):    [W, W]\n [Y, Y]\nLeft (L):  [B, R]\n [O, G]\nFront (F): [G, G]\n [O, O]\nRight (R): [O, G]\n [B, R]\nBack (B):  [R, R]\n [B, B]\nDown (D):  [W, W]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 20 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the cube, the front face has two green pieces on top that should be on the left face. Rotating the front face clockwise will move these pieces to the left face, aligning them with the correct color. Therefore, the next action should be to rotate the front face clockwise.</think><answer>F</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 1/20\n\nUp (U):    [W, W]\n [G, R]\nLeft (L):  [B, W]\n [O, W]\nFront (F): [O, G]\n [O, G]\nRight (R): [Y, G]\n [Y, R]\nBack (B):  [R, R]\n [B, B]\nDown (D):  [B, O]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 19 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the front face has two different colors, O and G. By applying the F action, I aim to rotate the front face clockwise, which should align the O colors on the front and the left faces, and the G colors on the front and the right faces, potentially simplifying the cube's state.</think><answer>F</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 2/20\n\nUp (U):    [W, W]\n [W, W]\nLeft (L):  [B, B]\n [O, O]\nFront (F): [O, O]\n [G, G]\nRight (R): [G, G]\n [R, R]\nBack (B):  [R, R]\n [B, B]\nDown (D):  [Y, Y]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 18 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the top face (U) is already uniform with white (W) tiles. To progress, I should start by moving the U face to see if this action aligns other colors correctly or sets up a sequence for future moves. Thus, rotating the U face is a logical first step.</think><answer>U</answer>\n", 1.0, "", "system\nYou're a helpful assistant. \nuser\nYou are solving a 2x2 Rubik's Cube (Pocket Cube). The goal is to restore the cube so that each of the faces consists of a single, unique color.\nAvailable actions use standard Singmaster notation for face rotations: U, U', D, D', L, L', R, R', F, F', B, B'.\n- Faces: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back).\n- Modifiers: A letter alone means 90\u00b0 clockwise (e.g., 'R'). A letter with prime (') means 90\u00b0 counter-clockwise (e.g., \"R'\").\nRespond with a sequence of actions separated by \"||\".\nExample: <answer>U</answer>\n\nYour available actions are:\nU, U', D, D', L, L', R, R', F, F', B, B'\nYou can make up to 20 actions, separated by the action separator \" || \"\n\nTurn 1:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 0/20\n\nUp (U):    [R, G]\n [G, W]\nLeft (L):  [G, O]\n [Y, Y]\nFront (F): [Y, R]\n [B, G]\nRight (R): [B, W]\n [R, W]\nBack (B):  [O, W]\n [O, O]\nDown (D):  [B, Y]\n [B, R]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 20 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the cube, the left face has two yellow pieces that should be on the down face. By rotating the left face clockwise (L), I can move these yellow pieces closer to their correct position on the down face.</think><answer>L</answer>\nuser\nReward:\n0.0\n\nTurn 2:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 1/20\n\nUp (U):    [O, G]\n [W, W]\nLeft (L):  [Y, G]\n [Y, O]\nFront (F): [R, R]\n [G, G]\nRight (R): [B, W]\n [R, W]\nBack (B):  [O, B]\n [O, B]\nDown (D):  [Y, Y]\n [B, R]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 19 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, my goal is to align the colors on each face. The back face has an 'O' and 'B' which need to be aligned with their respective faces. Executing 'B' will rotate the back face clockwise, potentially aligning the 'O' with the left face and the 'B' with the right face, moving me closer to solving the cube.</think><answer>B</answer>\nuser\nReward:\n0.0\n\nTurn 3:\nState:\n=== Rubik's Cube 2x2 State ===\nStep: 2/20\n\nUp (U):    [W, W]\n [W, W]\nLeft (L):  [G, G]\n [O, O]\nFront (F): [R, R]\n [G, G]\nRight (R): [B, B]\n [R, R]\nBack (B):  [O, O]\n [B, B]\nDown (D):  [Y, Y]\n [Y, Y]\n\nAvailable Actions:\nU, U', D, D', L, L', R, R', F, F', B, B'\n\nWhat is your next move?\nYou have 18 actions left. Always output: <think> [Your thoughts] </think> <answer> [your answer] </answer> with no extra text. Strictly follow this format. Max response length: 96 words (tokens).\n\nassistant\n<think>Given the current state of the Rubik's Cube, the Down (D) face is already correctly aligned with yellow (Y) on top. To progress, I need to consider moves that could potentially align other faces without disrupting the D face. A D' move will rotate the bottom layer clockwise, which could help in aligning the colors on the adjacent faces without affecting the already correct D face.</think><answer>D'</answer>\n", 1.0]]}