
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 $\overrightarrow{a}=(\cos \alpha,\sin \alpha)$ and $\overrightarrow{b}=(\cos \beta,\sin \beta)$, where $0 < \alpha < \beta < \pi$, if $|2\overrightarrow{a} + \overrightarrow{b}| = |\overrightarrow{a} - 2\overrightarrow{b}|$, calculate the value of $\beta - \alpha$.

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