
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
On a line segment $AB$ with a length of $12cm$, a point $C$ is randomly chosen. A rectangle is formed with $AC$ and $BC$ as adjacent sides. The probability that the area of this rectangle is greater than $32cm^2$ is ______.

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