
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 that $$\frac{\sin(\frac{3π}{2}-α)\cos(\frac{π}{2}+α)}{\cos(π-α)\sin(3π-α)\sin(-π-α)}$$=3, where α is an angle in the third quadrant, find the value of $\tanα$.
(2) Given that α is an angle in the second quadrant, find the value of $$\cosα \sqrt{1+\tan2α}+\sinα \sqrt{1+ \frac{1}{tan^{2}\alpha }}$$.

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