
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
Given the function $f(x)= \begin{cases} -x^{2}+x,x\leqslant 1 \\ \log _{ \frac {1}{3}}x,x > 1\end{cases}$, if the inequality $f(x)\leqslant \frac {5}{4}m-m^{2}$ holds for any $x∈R$, determine the range of the real number $m$.

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