
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 $\overrightarrow{a}=( \sqrt{2}\cos α, \sqrt{2}\sin α)$ and $\overrightarrow{b}=(\cos β, 2\sin β)$, with $\frac{π}{6}\leqslant α\leqslant \frac{π}{2} < β\leqslant \frac{5π}{6}$, calculate the value of $(β-α)$ given that $\overrightarrow{a} \perp (\overrightarrow{b} - \overrightarrow{a})$.

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