
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
Arrange the positive even numbers into groups according to the following rule: $\left(2\right)$, $\left(4,6\right)$, $\left(8,10,12\right)$, $\left(14,16,18,20\right)$, $\ldots$, we call "$4$" the first number in the second group, "$16$" the second number in the fourth group. If "$2024$" is the $m$-th number in the $n$-th group, then $m+n=\_\_\_\_\_\_$.

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