
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 number of sides of the second polygon is 4 more than the number of sides of the first polygon. The number of sides of the third polygon is 8 more than the number of sides of the second polygon, while the number of sides of the fourth polygon exceeds the number of sides of the third polygon by 1. The sum of the total number of diagonals of the first and fourth polygons is equal to the sum of the total number of diagonals of the second and third polygons. How many sides do these polygons have?

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