
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 that $α$ and $β$ are in the interval $(0, \dfrac {π}{2})$, and $3\sin ^{2}α+2\sin ^{2}β=1$, with $①3\sin 2α-2\sin 2β=0②$, find the value of $α+2β$.

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