
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

Circle $\omega_{1}$ and circle $\omega_{2}$ intersect at points $A$ and $B$. Let $PQ$ and $RS$ be the common external tangents to these two circles (where points $P$ and $R$ are on $\omega_{1}$, and points $Q$ and $S$ are on $\omega_{2}$). Given that $RB \parallel PQ$, and the ray $RB$ intersects circle $\omega_{2}$ at another point $W$, determine the ratio $\frac{RB}{BW}$.

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