
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 $x \in [1,2]$, $x^{2}-a \geqslant 0$", and the proposition $q$: "There exists $x_{0} \in \mathbb{R}$, such that $x_{0}^{2}+2ax_{0}+2-a=0$", if the proposition "$p$ and $q$" is true, then the range of the real number $a$ is ______.

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