
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 that the universal set $U = \mathbb{R}$, let the set $M$ be defined as $M = \{x \,|\, -1 \leq x \leq 4m - 2\}$, and the set $P$ be defined as $P = \{x \,|\, x > 2 \text{ or } x \leq 1\}$.
1. If $m = 2$, find the intersection $M \cap P$.
2. If the union of $M$ and $P$ is $\mathbb{R}$, find the range of the real number $m$.

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