
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
An isosceles triangle, a square, and a regular pentagon each have a perimeter of 20 inches. What is the ratio of the side length of the triangle (assuming both equal sides for simplicity) to the side length of the square? Express your answer as a common fraction.

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