
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 \(a_0=-3, b_0=2\), and for \(n\geq 0\), define:
\begin{align*}
a_{n+1} &= a_n + b_n + 2\sqrt{a_n^2 + b_n^2},\\
b_{n+1} &= a_n + b_n - 2\sqrt{a_n^2 + b_n^2}.
\end{align*}
Find \(\frac{1}{a_{2023}} + \frac{1}{b_{2023}}.\)

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