
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 positive integer and  $P$  a point in the plane. We wish to draw lines, none passing through  $P$ , in such a way that any ray starting from  $P$  intersects at least  $k$  of these lines. Determine the smallest number of lines needed.

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