
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 $$\tan\alpha=2$$, and $$\alpha\in\left(\pi, \frac{3\pi}{2}\right)$$,

(1) Find the values of $\sin\alpha$ and $\cos\alpha$.

(2) Calculate the value of $$\frac{\sin(\pi+\alpha)+2\sin\left(\frac{3\pi}{2}+\alpha\right)}{\cos(3\pi-\alpha)+1}$$.

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