
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 $B_{1}C_{2}$ and $C_{1}B_{2}$ intersect at point $K$. Find the measure (in degrees) of angle $B_{1}KB_{2}$.

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