
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 beam of light originates from point $A$ on a plane and is reflected several times between lines $AD$ and $CD$ before finally striking a point $B$ on line $CD$ at a $15^\circ$ angle and then reflecting back to point $A$. If the angle $\measuredangle CDA=10^\circ$, determine the maximum number of times the light can be reflected before striking $B$.

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