
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
Let $f(x)$ and $g(x)$ be two functions defined on the same interval $[a,b]$. If the function $y=f(x)-g(x)$ has two different zeros when $x \in [a,b]$, then $f(x)$ and $g(x)$ are called "associated functions" on the interval $[a,b]$, and the interval $[a,b]$ is called an "associated interval". If $f(x)=x^{2}-3x+4$ and $g(x)=2x+m$ are "associated functions" on $[0,3]$, then the range of $m$ is \_\_\_\_\_\_.

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