
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 regular nonagon (a 9-sided polygon) where two random lines formed by joining its vertices are chosen. These include sides and diagonals. What is the probability that the two randomly chosen lines intersect inside the nonagon?

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