
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
Points \(A\) and \(B\) are located in a plane such that the straight-line distance between them, \(AB\), is 10 units. Determine how many possible locations exist for point \(C\) in the same plane such that if triangle \(ABC\) forms, it would be a right triangle with an area of 20 square units.
A) 2
B) 4
C) 6
D) 8
E) 10

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