
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
A regular hexagon $B_1B_2B_3B_4B_5B_6$ is inscribed in a circle of area $\pi$. Point $Q$ lies inside the circle so that the region bounded by $\overline{QB_1}, \overline{QB_2},$ and the minor arc $\widehat{B_1B_2}$ of the circle has area $\frac{\pi}{12},$ while the region bounded by $\overline{QB_4}, \overline{QB_5},$ and the minor arc $\widehat{B_4B_5}$ of the circle has area $\frac{\pi}{18}.$ Compute the area of the region bounded by $\overline{QB_3}, \overline{QB_4},$ and the minor arc $\widehat{B_3B_4}$.

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