
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 $a \in \mathbb{R}$, let proposition $p$ be: "For all $x \in [1,2]$, $x^2 - a \geq 0$", and proposition $q$ be: "There exists an $x \in \mathbb{R}$ such that $x^2 + 2ax + 2 - a = 0$".  
(1) If proposition $p$ is true, find the range of values for the real number $a$.  
(2) If the proposition "$p \lor q$" is true and the proposition "$p \land q$" is false, find the range of values for the real number $a$.

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