
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
Simplify: $$\frac {1}{2 \sqrt {1}+ \sqrt {2}}$$+ $$\frac {1}{3 \sqrt {2}+2 \sqrt {3}}$$+……+ $$\frac {1}{(k+1) \sqrt {k}+k \sqrt {k+1}}$$+……+ $$\frac {1}{2019 \sqrt {2018}+2018 \sqrt {2019}}$$\=\_\_\_\_\_\_．

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