
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 ray of light originates from point $A$ in a prism shaped like a triangle, being reflected several times inside the prism before emerging out. If a ray makes $n$ reflections and $\measuredangle CDA=6^\circ$ for the prism, find the maximum possible number of internal reflections $n$ before the ray can emerge, assuming total internal reflection stops further internal reflections at or above $90^\circ$.
A) 12  
B) 14  
C) 15  
D) 16  
E) 20

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