
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 triangle has one leg of 15 inches and the hypotenuse of 34 inches. A second triangle, which is similar to the first, has a hypotenuse that is twice the length of the first triangle’s hypotenuse. What is the length of the second triangle's shortest leg, if the longer leg of the second triangle is 33% larger than the corresponding leg of the first triangle?

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