
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 8 numbers -3, -2, -1, 0, 1, 2, 3, 4, choose any 3 different numbers to form the coefficients a, b, c of the quadratic function $y=ax^2+bx+c$. Determine the number of possible combinations of a, b, c that ensure the origin is inside the parabola.

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