
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
Given an equilateral triangle $\mathrm{ABC}$. Right isosceles triangles ABP and BCQ with right angles at $\angle \mathrm{ABP}$ and $\angle \mathrm{BCQ}$ are constructed externally on sides $\mathrm{AB}$ and $\mathrm{BC}$, respectively. Find the angle $\angle \mathrm{PAQ}$.

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