
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 $p: \forall x \in \mathbb{R}$, $x^2 + a \geqslant 0$, and $q: \exists x \in \mathbb{R}$, such that $x^2 + (2+a)x + 1 = 0$. 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