
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
(The full score of this question is 12 points)  
Given proposition _p_: "For all _x_ in \[1,2\], _x_<sup>2</sup> - _a_ ≥ 0", and proposition _q_: "There exists _x_<sub>0</sub> in R, such that _x_<sup>2</sup> + 2_ax_<sub>0</sub> + 2 - _a_ = 0", if the proposition "_p_ and _q_" is true, find the range of the real number _a_.

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