
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 right $\triangle ABC$ with $\angle BAC = 90°$, the bisector of $\angle A$ meets side $BC$ at $D$, where $D$ is the midpoint of $BC$. The circle with center $B$ and radius $BD$ intersects side $AB$ at point $M$, and the circle with center $C$ and radius $CD$ intersects side $AC$ at point $N$. Determine the relationship between $\angle BMD$ and $\angle CND$.
A) $\angle BMD = 80°$ and $\angle CND = 90°$
B) $\angle BMD = \angle CND = 92°$
C) $\angle BMD = \angle CND = 45°$
D) $\angle BMD = \angle CND = 90°$

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