
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]


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Given a sequence ${{a_n}}$, its sum of the first $n$ terms is ${{S_n}}$. If ${{a_1}=2}$, ${{S_{n+1}}=\frac{n+2}{n}{{S_{n}}}}$, find the sum of the first $2018$ terms of the sequence ${\frac{1}{{{a_n}{a_{n+1}}}}}$.

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