
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
Two circles \(\sigma_{1}\) and \(\sigma_{2}\) intersect at points \(A\) and \(B\). Let \(P Q\) and \(R S\) be segments of the common external tangents to these circles (points \(P\) and \(R\) lie on \(\sigma_{1}\), and points \(Q\) and \(S\) lie on \(\sigma_{2}\)). It turns out that \(R B \parallel P Q\). The ray \(R B\) intersects \(\sigma_{2}\) a second time at point \(W\). Find the ratio \(R B / B W\).

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