
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 chord $ \left[AD\right]$ is perpendicular to the diameter $ \left[BC\right]$ of a circle, let $ E$ and $ F$ be the midpoints of the arcs $ AC$ and $ CD$, respectively. If $ AD\bigcap BE =\left\{G\right\}$, $ AF\bigcap BC=\left\{H\right\}$ and $ m(AC)=\alpha$, find the measure of angle $ \angle BHC$ in terms of $ \alpha$.

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