
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 the circle $x^2 + y^2 - 2x - 4y + \frac{19}{4} = 0$ at two points; Proposition $q$: $\exists x\_0 \in \left[-\frac{\pi}{6}, \frac{\pi}{4}\right], 2\sin\left(2x\_0 + \frac{\pi}{6}\right) + 2\cos 2x\_0 \leqslant m$.

1. Find the range of values for the real number $m$ if the proposition $p \land q$ is true.
2. Find the range of values for the real number $m$ if the proposition $p \lor q$ is true and the proposition $p \land q$ is false.

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