
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 function $f(x)=\cos 2x+2 \sqrt {3}\sin x\cos x(x\in R)$ with a maximum value of $M$ and smallest positive period of $T$.
(I) Find $M$ and $T$;
(II) If there are 10 distinct positive numbers $x_{i}$ that satisfy $f(x_{i})=M$, and $x_{i} < 10π (i=1,2,…,10)$, find the value of $x_{1}+x_{2}+…+x_{10}$.

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