
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
Two regular polygons with the same number of sides have sides 48 cm and 55 cm in length. What is the length of one side of another regular polygon with the same number of sides whose area is equal to the sum of the areas of the given polygons?

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