
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
On a plane, there are 100 points: \( O, A_{1}, A_{2}, \ldots, A_{99} \), where no three points are collinear. If there is a line passing through point \( O \) such that there are 48 points on one side of this line, is it possible to find a line also passing through point \( O \) such that there are (1) 49 points on one side? (2) 47 points on one side?

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