
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 rectangle with a side ratio of \(5:9\) is inscribed in a triangle whose base is 48 and height is 16, with the longer side of the rectangle lying on the base of the triangle. Find the sides of the rectangle.

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