
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 $\lfloor x \rfloor$ denote the greatest integer less than or equal to $x$, for example, $\lfloor 3 \rfloor = 3$, $\lfloor 1.2 \rfloor = 1$, $\lfloor -1.3 \rfloor = -2$. Given a sequence $\{a_n\}$ that satisfies $a_1=1$ and $a_{n+1}=a_n^2+a_n$, then $\left\lfloor \frac{a_1}{a_1+1}+\frac{a_2}{a_2+1}+\ldots+\frac{a_{2018}}{a_{2018}+1} \right\rfloor = \_ \_ \_ \_ \_ \_$.

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