
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
There are 100 distinct points on a plane and \( n \) different lines \( l_{1}, l_{2}, \cdots, l_{n} \). Let \( a_{k} \) denote the number of points through which the line \( l_{k} \) passes. If \( a_{1} + a_{2} + \cdots + a_{n} = 250 \), find the smallest possible value of \( n \).

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