
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
Consider a hexagon. How many diagonals does it have, i.e., straight lines connecting two non-adjacent vertices?

If this seems too easy, extend the six sides of the hexagon and determine how many points, other than the vertices of the hexagon, where all these lines (extended sides and diagonals) intersect?

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