
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
Two similar right triangles have areas of 30 square inches and 750 square inches, respectively. The length of the hypotenuse of the smaller triangle is 13 inches. What is the sum of the lengths of the legs of the larger triangle?

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