
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
Mathematicians invented a magic box, which produces a new rational number when any rational number pair $(a, b)$ is entered into it: $a^2 + b + 1$. For example, if the pair $(3, -2)$ is entered, it will produce $3^2 + (-2) + 1 = 8$. Now, if the rational number pair $(-2, 3)$ is entered into it to get a rational number $m$, and then the rational number pair $(m, 1)$ is entered, what is the resulting rational number?

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