
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 sum of the first 2017 terms of the sequence $\{c_{n}\}$ satisfies $S_{2017}$, and $c_{n} = \frac{1}{a_{n} + 1}$, where $a_{n+1} = a_{n}^{2} + a_{n}$ and $a_1 = \frac{1}{3}$. Calculate the integer part of $S_{2017}$.

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