
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
If the solutions of two linear equations differ by $1$, then the equation with the larger solution is called the "shifted equation" of the other equation. For example, the equation $x-2=0$ is the "shifted equation" of the equation $x-1=0$.

$(1)$ Determine whether the equation $2x+1=0$ is the "shifted equation" of the equation $2x+3=0$: ______; (Choose "yes" or "no")

$(2)$ If the equation in terms of $x$, $3\left(x-1\right)-m=\frac{m+3}{2}$ is the "shifted equation" of the equation in terms of $x$, $2\left(x-3\right)-1=3-\left(x+1\right)$, find the value of $n$.

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