
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
Consider five triangles drawn on a coordinate grid as follows. How many of these triangles are isosceles?
1. Triangle with vertices at (1, 2), (3, 2), and (2, 0)
2. Triangle with vertices at (4, 1), (4, 3), and (6, 1)
3. Triangle with vertices at (7, 2), (10, 2), and (8, 5)
4. Triangle with vertices at (0, 1), (3, 2), and (6, 1)
5. Triangle with vertices at (9, 1), (10, 3), and (11, 0)
A) 1
B) 2
C) 3
D) 4
E) 5

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