
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
In a polygon where all interior angles are equal, each interior angle is $20^\circ$ larger than three times its adjacent exterior angle. Find:<br/>
$(1)$ The number of sides of this polygon;<br/>
$(2)$ The sum of interior angles of the remaining polygon after cutting off one angle.

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