
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
A pyramid $PABCD$ has a rectangular base $ABCD$. Let $AB = 10$, $BC = 5$, $\overline{PA}$ is perpendicular to both $\overline{AD}$ and $\overline{AB}$, and the distance from vertex $P$ to vertex $B$ (line $PB$) is 20. Determine the volume of the pyramid $PABCD$.

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