
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 $f(x)=ax^{2}+bx+1$, where $a,b$ are real numbers and $x\in R$,
(1) If $f(x)$ has a zero point at $-1$, and the range of the function $f(x)$ is $[0,+\infty)$, find the analytical expression of $f(x)$;
(2) Under the conditions of (1), when $x\in[-2,2]$, $g(x)=f(x)-kx$ is a monotonic function, find the range of the real number $k$.

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