
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
The sequence $\left\{x_{n}\right\}$ satisfies: $x_{1}=\frac{1}{3}$, $x_{n+1}=x_{n}^{2}+x_{n}$. Calculate the integer part of the sum $\frac{1}{1+x_{1}}+\frac{1}{1+x_{2}}+\frac{1}{1+x_{3}}+\cdots +\frac{1}{1+x_{2015}}$.

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