
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given the cube \( C = \{(x, y, z) \mid 0 \leq x, y, z \leq 1 \} \) divided by the planes \( x = y \), \( y = z \), and \( z = x \), calculate the number of resulting parts.

Present the answer in LaTex format: \boxed{Your answer}
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