
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  $ABC$  be an isosceles triangle with  $AB=AC$  and incentre  $I$ . If  $AI=3$  and the distance from  $I$  to  $BC$  is  $2$ , what is the square of length on  $BC$ ?

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