
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 that $f$ is a mapping from set $M = \{a, b, c, d\}$ to set $N = \{0, 1, 2\}$, with $f(a) + f(b) + f(c) + f(d) = 4$, determine the number of different mappings.

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