
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 $\triangle ABC$, angle bisector of $\angle A$ meets side $BC$ at point $D$. A circle with center $D$ and radius $DB$ intersects the segments $AB$ and $AC$ at points $M$ and $N$ respectively. What is the measure of $\angle MDN$?
A) $90^\circ$
B) $180^\circ$
C) $120^\circ$
D) $45^\circ$
E) $60^\circ$

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