<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Given a cube with dimensions $12 \times 12 \times 12$, which is cut by planes parallel to the faces of the cube into unit cubes. Into how many parts will the cube be divided if a cross-section in the shape of a regular hexagon is made within it? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
216
Given a cube with dimensions $12 \times 12 \times 12$, which is cut by planes parallel to the faces of the cube into unit cubes. Into how many parts will the cube be divided if a cross-section in the shape of a regular hexagon is made within it?
test