
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
A rectangle has its area numerically equal to its perimeter. The rectangle’s length is three times its width. An equilateral triangle has its area numerically equal to half its perimeter. Compare the length of the rectangle's diagonal with the height of the equilateral triangle. Set up an equation to find the ratio of the length of the rectangle's diagonal to the height of the equilateral triangle.

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