
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
Let \( k \) be a given positive integer, and let \( P \) be a point on plane \( \alpha \). In plane \( \alpha \), if it is possible to draw \( n \) lines that do not pass through point \( P \) such that any ray starting from \( P \) and lying in this plane intersects with at least \( k \) of these \( n \) lines, find the minimum value of \( n \).

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