
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 
$$
f(x)= \begin{cases} 
x^{2} & \text{for } x\geq 0\\
x^{3}-(a-1)x+a^{2}-3a-4 & \text{for } x<0
\end{cases}
$$
is an increasing function on $(-\infty,+\infty)$, find the range of the real number $a$.

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