
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 different isosceles triangles with vertices among these seven points can be formed? Triangles that differ only in the order of the vertices are considered the same (for example, \( AOB \) and \( BOA \)).

The answer is 20.

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