
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
Let proposition p state, "For every $x \in \mathbb{R}$, $x^2 - 2x + m \geq 0$ always holds true," and let proposition q state, "The equation $\frac {x^{2}}{m-4}+ \frac {y^{2}}{6-m}=1$ represents a hyperbola."
(1) If p is false, determine the range of the real number m;
(2) If the statement $p \land q$ is false, while the statement $p \lor q$ is true, determine the range of the real number m.

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