
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
\( P \) is the midpoint of the height \( V O \) of the regular quadrilateral pyramid \( V-ABCD \). If the distance from point \( P \) to the side faces is 3, and the distance to the base is 5, what is the volume of the regular quadrilateral pyramid?

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