
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
Rectangle $ABCD$ is the base of pyramid $PABCD$. If $AB = 12$, $BC = 6$, $\overline{PA} \perp \overline{AB}$, $\overline{PA} \perp \overline{AD}$, and $PA = 10$, find the volume of $PABCD$. Additionally, compute the area of triangle $ABC$.

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