
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) Evaluate the integral $\int_{1}^{2}{\frac{1}{x}}dx=\_\_\_\_\_\_\_\_\_\_.$

(2) Given the arithmetic sequence $\{ a_{n} \}$ with the general term formula ${a_{n}}=3n-5$, the coefficient of the $x^{4}$ term in the expansion of ${{\left( 1+x \right)}^{5}}+{{\left( 1+x \right)}^{6}}+{{\left( 1+x \right)}^{7}}$ is the $\_\_\_\_\_\_\_\_\_$th term of the sequence.

(3) If the random variable $X$ follows a binomial distribution $X～B(4,p)$ and $E\left( X \right)=2,$ then $D\left( X \right)=\_\_\_\_\_\_\_\_\_\_.$

(4) Determine the value of $S= \sqrt{1+ \frac{1}{{1}^{2}}+ \frac{1}{{2}^{2}}}+ \sqrt{1+ \frac{1}{{2}^{2}}+ \frac{1}{{3}^{2}}}+...+ \sqrt{1+ \frac{1}{{2018}^{2}}+ \frac{1}{{2019}^{2}}}.$

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