
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 the function $f(x)=\left\{\begin{array}{l}{x}^{2}-5, x\geq 0\\ \frac{1}{x+1}, x<0\end{array}\right.$.<br/>$(1)$ If $f(m)=4$, find the value of the real number $m$;<br/>$(2)$ If $f(a) \lt -6$, find the range of the real number $a$.

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