
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 $g(x)=x^{2}-2 (x\in R)$, and $f(x)= \begin{cases} g(x)+x+4, x < g(x) \\ g(x)-x, x\geqslant g(x) \end{cases}$
1. Find $f(3)$
2. Find the range of the function $f(x)$.

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