
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 square grid with dimensions 10 by 10, determine how many of the following triangles are isosceles. Provide their coordinates:
1. Triangle with vertices at (2, 7), (5, 7), and (5, 3).
2. Triangle with vertices at (4, 2), (7, 2), and (4, 6).
3. Triangle with vertices at (2, 1), (2, 4), (7, 1).
4. Triangle with vertices at (7, 5), (9, 8), (9, 9).
5. Triangle with vertices at (8, 2), (8, 5), (10, 1).
A) 0
B) 1
C) 2
D) 3
E) 4

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