
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 the proposition p: For all $x$ in $\mathbb{R}$, $x^2 + kx + 2k + 5 \ge 0$; and the proposition q: There exists $k$ in $\mathbb{R}$ such that the equation $\frac {x^{2}}{4-k} + \frac {y^{2}}{k-1} = 1$ represents an ellipse with foci on the x-axis.
(1) If proposition q is true, determine the range of real numbers for $k$;
(2) If the proposition "p ∨ q" (p OR q) is true, and the proposition "p ∧ q" (p AND q) is false, determine the range of real numbers for $k$.

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