
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  $\triangle ABC$  be a triangle with  $AB=10$  and  $AC=16,$  and let  $I$  be the intersection of the internal angle bisectors of  $\triangle ABC.$  Suppose the tangents to the circumcircle of  $\triangle BIC$  at  $B$  and  $C$  intersect at a point  $P$  with  $PA=8.$  Compute the length of  ${BC}.$ *Proposed by Kyle Lee*

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