
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
If $\[x\}$ represents the maximum integer not exceeding $x$ (for example, $\[1.3]=1$, $\[-2\frac{1}{4}\]=-3$, etc.), then find the value of:
$$
\[ \frac{1}{2-\sqrt{1\times 2}}\]+\[ \frac{1}{3-\sqrt{2\times 3}}\]+\[ \frac{1}{4-\sqrt{3\times 4}}\]+\cdots +\[ \frac{1}{2018-\sqrt{2017\times 2018}}\]
$$

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