
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 two propositions:
P: The function $f(x) = x^2 - 2mx + 4$ $(m \in \mathbb{R})$ is monotonically increasing on the interval $[2, +\infty)$;
Q: The solution set for the inequality $4x^2 + 4(m-2)x + 1 > 0$ $(m \in \mathbb{R})$ is $\mathbb{R}$.

If $P \vee Q$ (P or Q) is true and $P \wedge Q$ (P and Q) is false, find the range of values for $m$.

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