
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) If the terminal side of angle $\theta$ passes through $P(-4t, 3t)$ ($t>0$), find the value of $2\sin\theta + \cos\theta$.  
(2) Given that a point $P$ on the terminal side of angle $\alpha$ has coordinates $(x, -\sqrt{3})$ ($x\neq 0$), and $\cos\alpha = \frac{\sqrt{2}}{4}x$, find $\sin\alpha$ and $\tan\alpha$.

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