
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
Given that a beam of light originates from a point $A$ and travels in a plane, being reflected multiple times between lines $AD$ and $CD$ before reaching point $B$, which lies on line $CD$, at a specific angle and then reflecting back to $A$, with $\measuredangle CDA=5^\circ$, calculate the maximum number of times, $n$, the light can reflect before reaching an angle of incidence at $B$ of $85^\circ$.

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