
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 $c= \frac {2}{\pi} \int_{ -1 }^{ 1 } \sqrt {1-x^{2}}dx$, the line $\sqrt {2}ax+by=2$ (where $a, b$ are non-zero real numbers) intersects with the circle $x^{2}+y^{2}=c$ ($c>0$) at points A and B, with O being the origin, and $\triangle AOB$ 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}
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