
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
(1) Given $\tan\alpha = 2$, find the value of $$\frac {\sin(2\pi - \alpha) + \cos(\pi + \alpha)}{\cos(\alpha - \pi) - \cos\left(\frac {3\pi}{2} - \alpha\right)}$$
(2) Simplify: $$\sin 50° (1+ \sqrt {3}\tan 10°)$$.

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