
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
What is the maximum number of diagonals of a regular  $12$ -gon which can be selected such that no two of the chosen diagonals are perpendicular?

Note: sides are not diagonals and diagonals which intersect outside the  $12$ -gon at right angles are still considered perpendicular.

*2018 CCA Math Bonanza Tiebreaker Round #1*

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