
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 and a rectangle have the same perimeter of 24 inches. The rectangle's length is twice its width. What is the ratio of the side length of the triangle to the width of the rectangle? Express your answer as a common fraction.

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