
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 the sequences \(\{a_n\}\) and \(\{b_n\}\) be defined such that \(a_0 = 2\), \(b_0 = 2\), and 

\[
\begin{cases}
a_{n+1} = a_n \sqrt{1 + a_n^2 + b_n^2} - b_n, \\
b_{n+1} = b_n \sqrt{1 + a_n^2 + b_n^2} + a_n.
\end{cases}
\]

Then find \(a_{2017}^2 + b_{2017}^2\).

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