
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
Xiao Ming and Xiao Hua simultaneously solve the system of equations $\left\{\begin{array}{l}mx+y=5\\ 2x-ny=13\end{array}\right.$. Xiao Ming made a mistake in observing $m$ and obtained the solution $\left\{\begin{array}{l}x=\frac{7}{2}\\ y=-2\end{array}\right.$. Xiao Hua made a mistake in observing $n$ and obtained the solution $\left\{\begin{array}{l}x=3\\ y=-7\end{array}\right.$. Then, the arithmetic square root of the sum of positive integer solutions of the inequality system $\left\{\begin{array}{l}t≤m+1\\ t>n\end{array}\right.$ with respect to $t$ is ____.

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