
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 triangle  $ABC$  we have  $|AB| \ne |AC|$ . The bisectors of  $\angle ABC$  and  $\angle  ACB$  meet  $AC$  and  $AB$  at  $E$  and  $F$ , respectively, and intersect at I. If  $|EI| = |FI|$  find the measure of  $\angle  BAC$ .

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