
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 Proposition P: The line $mx-y+2=0$ intersects with the circle $x^2+y^2-2x-4y+\frac{19}{4}=0$ at two points; and Proposition Q: $\exists x_0 \in \left[-\frac{\pi}{6}, \frac{\pi}{4}\right]$ such that $2\sin\left(2x_0+ \frac{\pi}{6}\right)+2\cos\left(2x_0\right) \leq m$.
(1) If the proposition $P \land Q$ is true, find the range of values for the real number $m$.
(2) If the proposition $P \lor Q$ is true and $P \land Q$ is false, find the range of values for the real number $m$.

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