
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  $ \omega_{1}$  and  $ \omega_{2}$  intersect in points  $ A$  and  $ B$ . Let  $ PQ$  and  $ RS$  be segments of common tangents to these circles (points  $ P$  and  $ R$  lie on   $ \omega_{1}$ , points  $ Q$  and  $ S$  lie on  $ \omega_{2}$ ). It appears that  $ RB\parallel PQ$ . Ray  $ RB$  intersects  $ \omega_{2}$   in a point  $ W\ne B$ . Find  $ RB/BW$ .

*S. Berlov*

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