
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 $\sin2\alpha = 2\sin\alpha\cos\alpha$, find: 
1. $\sin3\alpha = \_\_\_\_\_\_$ (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 $\sin18^\circ = \_\_\_\_\_\_$.

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