
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
Let the universal set be the set of real numbers $\mathbb{R}$, $A=\left\{x\mid 2x^{2}-7x+3\leqslant 0\right\}$, $B=\left\{x\mid x^{2}+a \lt 0\right\}$.
1. When $a=-4$, find $A\cap B$ and $A\cup B$;
2. If $\left(\complement _{\mathbb{R}}A\right)\cap B=B$, find the range of real numbers for $a$.

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