
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
Two right-angled triangles are similar. The larger triangle has short sides which are \(1 \text{ cm}\) and \(5 \text{ cm}\) longer than the short sides of the smaller triangle. The area of the larger triangle is \(8 \text{ cm}^2\) more than the area of the smaller triangle. Find all possible values for the side lengths of the short sides of the smaller triangle.

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