
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 equilateral triangle and a point M inside the triangle such that  $MA^2 = MB^2 +MC^2$ . Draw an equilateral triangle  $ACD$  where  $D \ne B$ . Let the point  $N$  inside  $\vartriangle ACD$  such that  $AMN$  is an equilateral triangle. Determine  $\angle BMC$ .



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