
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:
1. If $a_1$, $a_2$, $a_3 \in \mathbb{R}$, then $a_1^2+a_2^2+a_3^2 \geqslant a_1a_2+a_2a_3+a_1a_3$,
2. If $a_1$, $a_2$, $a_3$, $a_4 \in \mathbb{R}$, then $a_1^2+a_2^2+a_3^2+a_4^2 \geqslant \frac{2}{3}(a_1a_2+a_1a_3+a_1a_4+a_2a_3+a_2a_4+a_3a_4)$,

That is, the sum of the squares of three numbers is not less than the sum of the products of each pair of these three numbers; the sum of the squares of four numbers is not less than two-thirds of the sum of the products of each pair of these four numbers. Further generalizing a similar inequality about the sum of squares of $n$ numbers: If $a_1$, $a_2$, ..., $a_n \in \mathbb{R}$, then $a_1^2+a_2^2+…+a_n^2 \geqslant M(a_1a_2+a_1a_3+…+a_1a_n+a_2a_3+a_2a_4+…+a_{n-1}a_n) (n \in \mathbb{N}, n \geqslant 3)$, then $M=$ ______.

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