
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 square with area $16$ is inscribed in a square with area $25$, where each vertex of the smaller square touches a side of the larger square. One vertex of the smaller square divides a side of the larger square into two segments, and one length is three times the other length. Find the product of the lengths of the two segments.

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