
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 an acute triangle \( ABC \), angle \( A \) is \( 35^\circ \). Segments \( BB_1 \) and \( CC_1 \) are altitudes, points \( B_2 \) and \( C_2 \) are the midpoints of sides \( AC \) and \( AB \) respectively. Lines \( B_1C_2 \) and \( C_1B_2 \) intersect at point \( K \). Find the measure (in degrees) of angle \( B_1KB_2 \).

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