
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
Using the sum of sines formula $\sin (\alpha+\beta)=\sin \alpha\cos \beta+\cos \alpha\sin \beta$ and the double angle formula for sine $\sin 2\alpha=2\sin \alpha\cos \alpha$, find:  
① $\sin 3\alpha=$ ______ (expressed in terms of $\sin \alpha$);  
② Using the double and triple angle formulas and $\sin \alpha=\cos \left( \frac {\pi}{2}-\alpha\right)$, find $\sin 18^{\circ}=$ ______.

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