
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
From the set {1, 2, 3, 5, 7, 9, 0, -4, -6, -8}, select three different elements to serve as the values of A, B, and C in the equation $Ax^2 + By^2 = C$. Determine the number of different hyperbolas that this equation can represent.

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