
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
Reading and understanding:<br/>Definition: If the sum of the solutions of two linear equations is $1$, we call these two equations "beautiful equations."<br/>For example: The equation $2x-1=3$ has a solution of $x=2$, and the equation $x+1=0$ has a solution of $x=-1$. The sum of the solutions of these two equations is $1$, so these two equations are "beautiful equations."<br/>$(1)$ Please determine whether the equation $4x-\left(x+5\right)=1$ and the equation $-2y-y=3$ are "beautiful equations";<br/>$(2)$ If the equation about $x$ $\frac{x}{2}+m=0$ and the equation $3x=x+4$ are "beautiful equations," find the value of $m$.

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