
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
The sum of the angles of two polygons, expressed in degrees, is 21 times the sum of the total number of sides and diagonals, minus 39. The total number of diagonals is 99 more than the total number of sides. How many sides do the polygons have?

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