
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
Through point \( A \) located on a circle, a diameter \( AB \) and a chord \( AC \) are drawn, where \( AC = 8 \) and \( \angle BAC = 30^\circ \).

Find the length of the chord \( CM \), which is perpendicular to \( AB \).

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