
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
Determine how many triangles out of the six drawn on a 5x5 square grid are isosceles or equilateral. The triangles selected have the following vertices:
1. (0,5), (5,5), (2,2)
2. (1,1), (4,1), (4,4)
3. (1,4), (3,5), (5,4)
4. (1,0), (3,2), (5,0)
5. (0,2), (2,5), (4,2)
6. (2,1), (3,3), (4,1)
A) 2
B) 3
C) 4
D) 5
E) 6

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