
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 rectangle which has one side length double the other. One vertex of the square divides one of the shorter sides of the rectangle into two segments, one of length \( a \), and the other of length \( b \). The area of the rectangle is 18. Calculate the value of \( ab \).

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