
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
Let $\overrightarrow{a}=(3,-\sin 2x)$, $\overrightarrow{b}=(\cos 2x, \sqrt {3})$, $f(x)= \overrightarrow{a}\cdot \overrightarrow{b}$  
(Ⅰ) Find the smallest positive period of $f(x)$;  
(Ⅱ) Find the maximum value of $f(x)$ and the set of $x$ when the maximum value is achieved;  
(Ⅲ) Find the value of angle $\alpha$ that satisfies $f(\alpha)=- \sqrt {3}$ and $0 < \alpha < \pi$.

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