
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 difference in the number of sides of two regular polygons is 10. The difference in the number of their diagonals is 15 less than the degree measure of one angle of the polygon with the fewer sides. How many sides do these polygons have?

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