
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 sets $A=\{x|x^{2}-3x-4 \lt 0\}$ and $B=\{x|x^{2}+4mx-5m^{2} \lt 0}$.<br/>$(1)$ If set $B=\{x\left|\right.-5 \lt x \lt 1\}$, find the value of the real number $m$ in this case;<br/>$(2)$ Given proposition $p:x\in A$, proposition $q:x\in B$, if $p$ is a sufficient condition for $q$, find the range of real numbers $m$.

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