
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
The side \( AB \) of a regular hexagon \( ABCDEF \) is equal to \( \sqrt{3} \) and serves as a chord of a certain circle, while the other sides of the hexagon lie outside this circle. The length of the tangent \( CM \), drawn to the same circle from vertex \( C \), is 3. Find the diameter of the circle.

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