
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
$A B C D E F$ is a regular hexagon, and point O is its center. How many distinct isosceles triangles with vertices at these seven points (A, B, C, D, E, F, O) can be formed? Triangles that differ only by the order of their vertices are considered the same (for example, AOB and BOA).

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