
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]


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Let \( W \) be the hypercube \(\left\{\left(x_{1}, x_{2}, x_{3}, x_{4}\right) \mid 0 \leq x_{1}, x_{2}, x_{3}, x_{4} \leq 1\right\}\). The intersection of \( W \) and a hyperplane parallel to \( x_{1}+x_{2}+x_{3}+x_{4}=0 \) is a non-degenerate 3-dimensional polyhedron. What is the maximum number of faces of this polyhedron?

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