
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 the interval [1,2], $x^2 - a \geq 0$", and q: "There exists an $x$ in $\mathbb{R}$ such that $x^2 + 2ax + (2-a) = 0$", if the compound proposition "p and q" is true, determine the range of the real number $a$.

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