
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]


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A square with vertices \((-b, -b), (b, -b), (-b, b), (b, b)\) is intersected by the line \( y = \frac{x}{3} \). Find the perimeter of one of the resulting quadrilaterals, divided by \( b \), and express your answer in simplified radical form.

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