
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 $f(x)=2\sin ( \frac {πx}{6}+ \frac {π}{3})(0\leqslant x\leqslant 5)$, points $A$ and $B$ are the highest and lowest points on the graph of $y=f(x)$, respectively.
(1) Find the coordinates of points $A$ and $B$ and the value of $\overrightarrow{OA}\cdot \overrightarrow{OB}$;
(2) If points $A$ and $B$ are on the terminal sides of angles $α$ and $β$, respectively, find the value of $\tan (α-2β)$.

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