
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 function $f(x)=x^2-1$. For any $x \in \left[ \frac{2}{3}, +\infty \right)$, the inequality $f\left( \frac{x}{m} \right) - 4m^2f(x) \leqslant f(x-1) + 4f(m)$ always holds. Then, the range of the real number $m$ is.

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