
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
In the sequences $\{a_n\}$ and $\{b_n\}$, it is given that $a_{n+1} = a_n + b_n + \sqrt{a_n^2 + b_n^2}$, $b_{n+1} = a_n + b_n - \sqrt{a_n^2 + b_n^2}$, with $a_1 = 1$, $b_1 = 1$. Let $c_n = \frac{1}{a_n} + \frac{1}{b_n}$. Find the sum of the first 2017 terms of the sequence $\{c_n\}$.

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