
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) Use the Horner's method to calculate the value of the function $f(x)=2x^{5}-3x^{3}+2x^{2}+x-3$, if $x=2$, then the value of $V_{3}$ is ______.

(2) If the proposition “$\exists t \in \mathbb{R}, t^{2}-2t-a < 0$” is a false proposition, then the range of the real number $a$ is ______.

(3) Given that the line $y=x-1$ intersects with the ellipse $\frac{x^{2}}{4}+ \frac{y^{2}}{3}=1$ at points $A$ and $B$, then the length of segment $AB$ is ______.

(4) If $f(x)=- \frac{1}{2}x^{2}+b\ln (2x+4)$ is a decreasing function on $(-2,+\infty)$, then the range of $b$ is ______.

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