
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 areas of the larger triangle to the smaller triangle is 9, and the difference in their areas is 50 square feet. One side of the smaller triangle measures 5 feet. Find the length of the corresponding side of the larger triangle.

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