
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 that the proposition "The equation $x^{2}+mx+2m+5=0$ has two distinct real roots with respect to $x$" is false.<br/>$(1)$ Find the set $A$ of real numbers $m$; <br/>$(2)$ Let $B=\{x\left|\right.1-2a\leqslant x\leqslant a-1\}$, if $x\in A$ is a sufficient but not necessary condition for $x\in B$, find the range of real number $a$.

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