
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 p: "For all $x$ in $\mathbb{R}$, the inequality $x^2 + mx + \frac{m}{2} + 2 \geq 0$ always holds true"; q: "The distance from the focus of the parabola $y^2 = 2mx$ (where $m > 0$) to its directrix is greater than 1." If $p \lor q$ is a true statement and $p \land q$ is false, find the range of real numbers $m$.

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