
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 the cosine formula for the sum of two angles $C_{(α+β)}$: $\cos (α-β)=\cos α\cos β-\sin α\sin β$;
1. Derive the sine formula for the sum of two angles $S_{(α+β)}$: $\sin (α+β)=$ ________
2. If $\cos α=- \frac {4}{5}$, $α∈(π, \frac {3}{2}π)$, and $\tan β=- \frac {1}{3}$, $β∈( \frac {π}{2},π)$, find $\sin (α+β)$.

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