
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 \(ABC\), the perpendicular bisectors of sides \(AB\) and \(AC\) are drawn, intersecting lines \(AC\) and \(AB\) at points \(N\) and \(M\) respectively. The length of segment \(NM\) is equal to the length of side \(BC\) of the triangle. The angle at vertex \(C\) of the triangle is \(40^\circ\). Find the angle at vertex \(B\) of the triangle.

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