
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 that $a_1$, $a_2$, $a_3$ are not all zero, let $x$, $y$ be positive numbers satisfying $x^2+y^2=2$. Define $$\frac {xa_{1}a_{2}+ya_{2}a_{3}}{ a_{ 1 }^{ 2 }+ a_{ 2 }^{ 2 }+ a_{ 3 }^{ 2 }}$$ to be less than or equal to $M$, then the minimum value of $M$ is \_\_\_\_\_\_.

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