
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
Recall that the sum of the angles of a triangle is 180 degrees. In triangle $ABC$, angle $A$ is a right angle. Let $BM$ be the median of the triangle and $D$ be the midpoint of $BM$. It turns out that $\angle ABD = \angle ACD$. What are the measures of these angles?

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