
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
V is the pyramidal region defined by the inequalities \( x, y, z \geq 0 \) and \( x + y + z \leq 1 \). Evaluate the integral:

\[ \int_V x y^9 z^8 (1 - x - y - z)^4 \, dx \, dy \, dz. \

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