
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
In acute  $\triangle ABC,$  let  $I$  denote the incenter and suppose that line  $AI$  intersects segment  $BC$  at a point  $D.$  Given that  $AI=3, ID=2,$  and  $BI^2+CI^2=64,$  compute  $BC^2.$ *Proposed by Kyle Lee*

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