
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 line, 100 points are marked, and one additional point is marked outside the line. Consider all the triangles with vertices at these points.

What is the maximum number of them that can be isosceles?

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