
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 every $x$ in the interval $[1,2]$, it is true that $x^2 \geq a$." There is also a proposition q: "There exists an $x_0$ in $\mathbb{R}$ such that the equation $x_0^2 + 2ax_0 + 2 - a = 0$ is satisfied." If the compound proposition "p ∧ q" (p AND q) is true, then the range of values for the real number $a$ is _____________.

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