
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  $n$  be the number of isosceles triangles whose vertices are also the vertices of a regular 2019-gon.
Then the remainder when  $n$  is divided by 100
[list=1]
[*] 15
[*] 25
[*] 35
[*] 65
[/list]

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