
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
Given a triangle \( \triangle ABC \) with \( D \) as the incenter. Let \( E \) be the incenter of \( \triangle ABD \) and \( F \) be the incenter of \( \triangle BDE \). If the measure of angle \( \angle BFE \) is an integer, find the minimum value of \( \angle BFE \).

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