
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 laser beam originates from point $A$ and travels in a plane, being reflected $n$ times between lines $AD$ and $CD$ before hitting a point $B$ (which may be on $AD$ or $CD$) perpendicularly and then retracing its path back to $A$. Each point of reflection on $AD$ and $CD$ shows the beam forming equal angles with the line. Given that $\measuredangle CDA = 15^\circ$, determine the largest possible value of $n$.

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