
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
The ratio of the area of the larger triangle to the smaller triangle is the square of an integer, and the area difference is 18 square feet. If the smaller triangle has a side of 3 feet, determine the length of the corresponding side of the larger triangle in feet.

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