
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
$M$ is the midpoint of the height $B D$ in an isosceles triangle $A B C$. Point $M$ serves as the center of a circle with radius $M D$. Find the angular measure of the arc of the circle enclosed between the sides $B A$ and $B C$, given that $\angle B A C = 65^{\circ}$.

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