
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: For all $x \in \mathbb{R}$, the inequality $x^2 + 1 \geq a$ holds true;
q: The equation $(\rho \cos \alpha)^2 - (\rho \sin \alpha)^2 = a + 2$ represents a hyperbola with foci on the x-axis.

(Ⅰ) If proposition p is true, determine the range of values for the real number $a$.
(Ⅱ) If "p and q" are both true propositions, determine the range of values for the real number $a$.

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