
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
(1) The negation of the proposition: "There exists $x_0 > -1$ such that $x_0^2+x_0-2018 > 0$" is _______________.

(2) The standard equation of the ellipse passing through $A(-2,0)$ with eccentricity $e=\frac{1}{2}$ and its foci on the $x$-axis is _______________.

(3) The minimum value of the function $f(x)= \frac{1}{3}x^3+x^2-3x-4$ on the interval $[0,2]$ is _______________.

(4) On the parabola $y^2=8x$, there are two points $A(x_1,y_1)$ and $B(x_2,y_2)$, and $x_1+x_2=10$. If the focus of the parabola is $F$, then $|FA|+|FB|=$ _______________.

(5) If $f(x)=2xf'(1)+x^2$, then $f'(-1)=$ _______________.

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