
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
In how many different ways can integers \( a, b, c \in [1, 100] \) be chosen such that the points with coordinates \( A(-1, a), B(0, b) \), and \( C(1, c) \) form a right triangle?

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