
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 $a$ is a real number, let $A=\{x|2x+a\geqslant x^{2}\}$.<br/>$(1)$ When $a=8$, represent the set $A$ using intervals;<br/>$(2)$ Let $B=\{x\left|\right.\lg x=0\}$, if $B\subseteq A$, find the range of real numbers for $a$.

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