
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 that the terminal side of angle $\alpha$ intersects the unit circle at point P with coordinates $\left(-\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)$,

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

(2) Calculate the value of $\frac{\sin(\alpha-\pi)+\cos(\alpha+ \frac{\pi}{2})}{\tan(\pi+\alpha)}$,

(3) Determine the sign of $\tan(\alpha+ \frac{\pi}{4})$ and explain the reason.

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