
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
We colour all the sides and diagonals of a regular polygon  $P$  with  $43$  vertices either
red or blue in such a way that every vertex is an endpoint of  $20$  red segments and  $22$  blue segments.
A triangle formed by vertices of  $P$  is called monochromatic if all of its sides have the same colour.
Suppose that there are  $2022$  blue monochromatic triangles. How many red monochromatic triangles
are there?


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