
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, and $\triangle AOB$ is a right-angled triangle, then the minimum value of $\dfrac{1}{a^{2}}+ \dfrac{2}{b^{2}}$ is \_\_\_\_\_\_.

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