
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 has vertices at $(-b, -b), (b, -b), (-b, b), (b, b)$. The square is cut by the line $y = 2x$. What is the perimeter of one of the resulting congruent quadrilaterals, divided by $b$, when expressed in simplified radical form?

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