
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 that $\triangle B_1B_2B_3$ is an isosceles triangle with $B_1B_2 = B_2B_3$ and $\angle B_2 = 100^\circ$, point $B_{n+3}$ is defined as the midpoint of segment $B_nB_{n+1}$ for all positive integers $n$. Determine the measure of $\measuredangle B_{10}B_{11}B_9$.

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