
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 $PABCD$ where $AB = 10$, $BC = 5$. The line segment $\overline{PA}$ is perpendicular to both $\overline{AD}$ and $\overline{AB}$, and $\overline{PC}$ is perpendicular to $\overline{CD}$. If $PB = 20$, determine the volume of pyramid $PABCD$.

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