
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
In the isosceles right triangle \(AOB\), points \(P, Q, R,\) and \(S\) are chosen on the sides \(OB, OA,\) and \(AB\) respectively, such that \(PQRS\) forms a square. If the lengths of \(OP\) and \(OQ\) are \(a\) and \(b\) respectively, and the area of the square \(PQRS\) is \(\frac{2}{5}\) of the area of the triangle \(AOB\), determine the value of \(\frac{a}{b}\).

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