
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 \(n \geq 0\), let
\[ a_{n+1} = a_n + b_n + \sqrt{a_n^2 + b_n^2}, \]
\[ b_{n+1} = a_n + b_n - \sqrt{a_n^2 + b_n^2}. \]
Find \(\frac{1}{a_{10}} + \frac{1}{b_{10}}\).

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