
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 an area of $16$ is inscribed in another square whose area is $18$. At each point where a vertex of the smaller square touches the bigger square, the side of the larger square is divided into two segments: one of length $a$ and the other of length $b$. Find the product $ab$.
A) -5
B) -7
C) -10
D) 0
E) 2

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