
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 a quadratic function $f(x)=ax^{2}+bx+c(a\neq 0)$ whose graph passes through the point $(0,1)$, and has a unique zero point $(-1)$.
(I) Find the expression of $f(x)$;
(II) When $x\in[-2,2]$, find the minimum value $g(k)$ of the function $F(x)=f(x)-kx$.

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