
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 \( A B C \). Points \( D \) and \( E \) are taken on side \( A C \), and then segments \( B D \) and \( B E \) are drawn, dividing triangle \( A B C \) into three triangles, one of which is equilateral, and the other two are isosceles. Find the measure of angle \( B \). It is assumed that the sum of the angles of a triangle is 180 degrees.

If there are multiple answers, list all possible answers separated by commas or semicolons.

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