
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
For the interval $\left[a,b\right]\left(a \lt b\right)$, if the function $y=f\left(x\right)$ satisfies the following conditions simultaneously: ① $f\left(x\right)$ is a monotonic function on $\left[a,b\right]$; ② the range of the function $y=f\left(x\right)$ for $x\in \left[a,b\right]$ is $\left[a,b\right]$, then the interval $\left[a,b\right]$ is called the "maintaining value" interval of the function $f\left(x\right)$. (1) Write down a "maintaining value" interval for the function $y=2x^{2}$ as ______; (2) If the function $f\left(x\right)=mx^{2}-3x+4\left(m \gt 0\right)$ has a "maintaining value" interval, then the range of the real number $m$ is ______.

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