
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 vectors $\overrightarrow{a}=(2\cos \alpha, \sqrt{2}\sin \alpha)$ and $\overrightarrow{b}=(2\cos \beta,2\sin \beta)$, with the constraints $\frac{\pi}{6}\leqslant \alpha < \frac{\pi}{2} < \beta\leqslant \frac{5\pi}{6}$, if $\overrightarrow{a}\perp( \overrightarrow{b}- \overrightarrow{a})$, calculate the value of $\beta-\alpha$.

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