
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 sets $A=\{x_1, x_2, \ldots, x_n\}$ and $B=\{y_1, y_2, \ldots, y_m\}$, where $n, m \in \mathbb{N}^+$, if $x_1+x_2+\ldots+x_n = y_1+y_2+\ldots+y_m$, then sets $A$ and $B$ are called equal-sum sets. Given that sets $M$ and $N$, which consist of positive integers, are equal-sum sets, and set $M=\{1, 2, 3\}$, determine the number of possible sets $N$.

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