
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
Will stands at a point \( P \) on the edge of a circular room with perfectly reflective walls. He shines two laser pointers into the room, forming angles of \( n^\circ \) and \( (n+1)^\circ \) with the tangent at \( P \), where \( n \) is a positive integer less than 90. The lasers reflect off the walls, illuminating the points they hit on the walls, until they reach \( P \) again ( \( P \) is also illuminated at the end). What is the minimum possible number of illuminated points on the walls of the room?

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