
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 the interval [1, 2], $x^2 - a \geq 0$", and proposition q: "The equation $x^2 + 2ax + a + 2 = 0$ has a solution." If the proposition "p and q" is true, determine the range of values for the real number a.

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