
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-angled triangle $ABC$, angle $A$ is $35^\circ$. The segments $BB_1$ and $CC_1$ are altitudes, points $B_2$ and $C_2$ are the midpoints of sides $AC$ and $AB$ respectively. The 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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