
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]


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Select three different numbers from -1, 0, 1, 2 to serve as the coefficients (a, b, c) of the quadratic function $f(x) = ax^2 + bx + c$. There are a total of $\boxed{18}$ different quadratic functions that can be formed, among which $\boxed{6}$ are even functions.

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