
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 propositions $p$ and $q$: $p$ states that the real number $x$ satisfies $|2x - m| \geqslant 1$, and $q$ states that the real number $x$ satisfies $\frac{1 - 3x}{x + 2} > 0$.
1. When $m = 1$, find the range of real number $x$ that makes proposition $p \land q$ true.
2. If $\lnot p$ is a necessary but not sufficient condition for $q$, find the range of real number $m$.

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