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

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