
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
We define that if the solution to the one-variable linear equation $ax=b$ with respect to $x$ is $b+a$, then the equation is called a "sum solution equation". For example, the solution to $2x=-4$ is $-2$, and $-2=-4+2$, so the equation $2x=-4$ is a sum solution equation. Please answer the following questions according to the above rules:
- $(1)$ Determine whether $3x=4.5$ is a sum solution equation;
- $(2)$ If the one-variable linear equation $5x=m+1$ with respect to $x$ is a sum solution equation, find the value of $m$.

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