
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 $f(x)$ be a function defined on $\mathbb{R}$ such that $f(-x) + f(x) = 0$ for all x, and for any $x_1, x_2 \in \mathbb{R}$, the inequality $(x_1 - x_2)[f(x_1) - f(x_2)] < 0$ holds. If $f(2t^2 - 4) + f(4m - 2t) \geq f(0)$ for all $t \in [0, 2]$, determine the range of values for $m$.

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