
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 light ray begins at point $A$ in a plane, and reflects multiple times between two lines, $PQ$ and $RS$, before hitting a target point $B$ such that it strikes $B$ perpendicularly and returns to $A$. Given $\measuredangle QRS = 10^\circ$, calculate the maximum number of reflections, $n$, before the ray is perpendicular to $B$, and find the distance from the last point of reflection on line $RS$ to $B$ if it is 3 units past the point of perpendicular strike.
A) 7
B) 8
C) 9
D) 10
E) No maximum number

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