
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 square $ABCD$ with side length $24$ cm. Diagonals $\overline{AC}$ and $\overline{BD}$ intersect at point $O$. If we remove triangle $ABO$ from the square and then fold along lines $\overline{AO}$ and $\overline{BO}$ such that they meet at point $P$ above the base, thus forming a square-based pyramid where $AP = BP = OP = \sqrt{364} \text{ cm}$. Determine the volume of this pyramid.

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