
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
Consider a four-dimensional solid $T$ consisting of all points $(x,y,z,w)$ in 4D space such that: $|x| + |y| \leq 1$, $|x| + |z| \leq 1$, $|y| + |z| \leq 1$, and $|x| + |w| \leq 1$. Find the hypervolume of $T$.

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