
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
If the function $y=f\left(x\right)$ has a point $x_{0}\in \left[a,b\right]$ on the interval $\left[a,b\right]$ such that $f({x}_{0})=\frac{f(b)-f(a)}{b-a}$, then $x_{0}$ is called a mean value point of the function $y=f\left(x\right)$ on the interval $\left[a,b\right]$. Given that the function $y=3^{2x}-3^{x+1}-m$ has a mean value point on $\left[0,1\right]$, the range of real number $m$ is ______.

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