
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 \(ABC\), the measure of angle \(A\) is 30 degrees, and the length of the median drawn from vertex \(B\) is equal to the length of the altitude drawn from vertex \(C\). Find the measures of angles \(B\) and \(C\).

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