
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
In a right triangle \( A B C \), there is a rectangle \( E K M R \) positioned such that side \( E K \) lies on the hypotenuse \( B C \), and vertices \( M \) and \( P \) are on the legs \( A C \) and \( A B \), respectively. The leg \( A C \) is 3, and the leg \( A B \) is 4. Find the sides of the rectangle \( E K M R \) given that its area is \( \frac{3}{5} \) and its perimeter is less than 9.

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