
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 length of the median to the hypotenuse of a scalene right triangle is $15$ units. The hypotenuse is three times the length of the shorter leg of the triangle. What is the length of the shorter leg of the triangle, in units?

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