
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 two sets $M = \{1, 2, 3, m\}$ and $N = \{4, 7, n^4, n^2 + 3n\}$ where $m, n \in \mathbb{N}$, the mapping $f: y \mapsto 3x + 1$ is a function from $M$ to $N$. Determine the value of $m - n$.

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