
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
Given the sets $M=\{a, b, c\}$ and $N=\{-1, 0, 1\}$, a mapping from $M$ to $N$ satisfies $f(a) + f(b) + f(c) = 0$. Calculate the number of such mappings $f$.

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