
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 right isosceles triangle and a rectangle (with one side twice as long as the other) both have perimeters of 48 inches. What is the ratio of the length of the hypotenuse of the triangle to the shorter side of the rectangle? Express your answer as a common fraction.

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