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

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