
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: if the solution to the one-variable linear equation $ax=b$ in terms of $x$ is $x=b-a$, then the equation is called a "difference solution equation". For example, the solution to $2x=4$ is $x=2$, and $2=4-2$, so the equation $2x=4$ is a difference solution equation.  
$(1)$ Determine whether the equation $3x=4.5$ is a difference solution equation;  
$(2)$ If the one-variable linear equation $5x-m=1$ in terms of $x$ is a difference solution equation, find the value of $m$.

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