
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 proposition p: "For all $x \in [1, 2]$, $x^2 - a \geq 0$", and proposition q: "The equation $x^2 + 2ax + 2 - a = 0$ has real roots", determine the range of the real number $a$ if the proposition "$\neg p \lor \neg q$" is false.

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