
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
Given the line $\sqrt{2}ax+by=2$ (where $a$ and $b$ are non-zero real numbers) intersects the circle $x^2+y^2=1$ at points A and B, and O is the origin, with $\triangle AOB$ being a right-angled triangle, the minimum value of $\frac{1}{a^2} + \frac{2}{b^2}$ is \_\_\_\_\_\_.

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