
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 \(c_0 = -3, d_0 = 2\), and for \(n \geq 0\), let
\begin{align*}
c_{n+1} &= c_n + d_n + 2\sqrt{c_n^2 + d_n^2}, \\
d_{n+1} &= c_n + d_n - 2\sqrt{c_n^2 + d_n^2}.
\end{align*}
Calculate \(\frac{1}{c_{2012}} + \frac{1}{d_{2012}}\).

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