
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
Points $A$, $B$, $C$, and $P$ are in space such that each of $\overline{PA}$, $\overline{PB}$, and $\overline{PC}$ is perpendicular to the other two. If $PA = PB = 12$ and $PC = 7$, what is the volume of pyramid $PABC$?

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