
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
Let $[x]$ denote the greatest integer that does not exceed the real number $x$. Find the smallest positive integer $n$ such that
$$
\left[\frac{\sqrt{n+1}-\sqrt{n}}{\sqrt{4n^2+4n+1}-\sqrt{4n^2+4n}}\right] 
= [\sqrt{4n+2018}].
$$

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