
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 equation $x^2 + mx + 1 = 0$ has two distinct negative real roots, and proposition $q$: $\forall x \in \mathbb{R}, 4x^2 + 4(m-2)x + 1 > 0$ always holds; if $p$ or $q$ is true, and $p$ and $q$ are false, find the range of the real number $m$.

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