
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 $ \alpha $ is an angle in the fourth quadrant, and $ \cos \alpha = \frac{3}{5} $.
(1) Find the value of $ \tan \alpha $;
(2) Calculate the value of $ \frac{ \sin\left(\frac{3}{2}\pi - \alpha\right) + 2\cos\left(\alpha + \frac{\pi}{2}\right)}{\sin\left(\alpha - \pi\right) - 3\cos\left(2\pi - \alpha\right)} $.

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