
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 convex nonagon (nine-sided polygon) has exactly one pair of vertices that form an isosceles triangle with the center of the polygon. How many diagonals does this nonagon have?

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