
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 $a\in \mathbf{R}$, let proposition $p$ be "$\forall x\in [1,2], x^{2}-a\geqslant 0$", and proposition $q$ be "$\exists x\in \mathbf{R}, x^{2}+2ax+2-a=0$".

(1) If proposition $p$ is true, find the range of the real number $a$.

(2) If the proposition "$p$ or $q$" is true, and the proposition "$p$ and $q$" is false, find the range of the real number $a$.

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