
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 equilateral triangle has a perimeter of 48 inches. A square and a rectangle are such that the square’s perimeter is 64 inches and the rectangle’s perimeter is twice the perimeter of the square. What is the ratio of the length of the side of the triangle to the length of the side of the square? Express your answer as a common fraction.

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