
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
Given a right triangle \(ABC\) with the right angle at vertex \(B\). A median \(BD\) is drawn from vertex \(B\) to the hypotenuse \(AC\). Let \(K\) be the point of tangency of the side \(AD\) of triangle \(ABD\) with the circle inscribed in this triangle.

Find the angles of triangle \(ABC\) if \(K\) bisects \(AD\).

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