
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 is inscribed in a right triangle with a hypotenuse of 24 cm and an angle of $60^{\circ}$. The base of the rectangle lies on the hypotenuse. What should the lengths of the sides of the rectangle be in order for its area to be the largest?

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