
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
Let $\triangle XYZ$ be an equilateral triangle with side length $s$. Point $P$ is a point inside $\triangle XYZ$, specifically at one third of the height from base $XY$ to vertex $Z$. If we extend rays $PX$ and $PY$, and place points $A$ and $B$ respectively on these rays such that $\overline{PA}$ and $\overline{PB}$ are equal in length to each side of the triangle, find the angle $\angle APB$.

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