
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
Isosceles right triangle $PQR$ (with $\angle PQR = \angle PRQ = 45^\circ$ and hypotenuse $\overline{PQ}$) encloses a right triangle $ABC$ (hypotenuse $\overline{AB}$) as shown. Given $PC = 5$ and $BP = CQ = 4$, compute $AQ$.

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