
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 triangle $ABC$, where $AB = AC$, has been folded so that vertex $A$ now rests at $A'$ on $\overline{BC}$, such that $BA' = 3$ and $A'C = 5$. The original length of each equal side of the triangle is 10. Find the length of the crease $\overline{PQ}$.

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