
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 $q$ as follows:
- Proposition $p$: The domain of the function $f(x) = \lg(-mx^2 + 2x - m)$ is $\mathbb{R}$;
- Proposition $q$: The slope of the tangent line at any point on the graph of the function $g(x) = 4\ln{x} + \frac{1}{2}x^2 - (m - 1)x$ is always greater than $2$,

Find the range of the real number $m$ if "$p \lor q$" is a true proposition and "$p \land q$" is a false proposition.

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