
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
Let the function $g(x)=x^2-2$ ($x \in \mathbb{R}$), and $$f(x)= \begin{cases} g(x)+x+4, & x<g(x) \\ g(x)-x, & x\geq g(x)\end{cases}$$ Then, the range of $f(x)$ is __________.

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