
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 the domain of the function $f(x)$ be $R$, and $f(x)=\frac{1}{3}f({x+1})$. When $x\in \left(-1,0\right]$, $f\left(x\right)=x\left(x+1\right)$. If for any $x\in \left(-\infty ,m\right]$, $f(x)≥-\frac{{81}}{{16}}$, find the range of the real number $m$.

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