
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 $f(x) = mx^2 + (1-3m)x - 4$, where $m \in \mathbb{R}$.
- (I) When $m=1$, find the maximum and minimum values of $f(x)$ in the interval $[-2, 2]$.
- (II) Solve the inequality $f(x) > -1$.
- (III) When $m < 0$, if there exists $x_0 \in (1, +\infty)$ such that $f(x_0) > 0$, find the range of $m$.

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