
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 9 is inscribed in a square with area 16, such that each vertex of the smaller square is on a side of the larger square. Let's say two consecutive vertices of the smaller square divide two sides of the larger square into segments of lengths a and b, respectively. Determine the product ab.

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