
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 $$tan(α+β)=2tanβ (α，β≠ \frac {kπ}{2}，k∈Z)$$, find the value of $$\frac {sin(α+2β)}{sin\alpha }$$.

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