
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 $90^\circ < \alpha < 180^\circ$, and a point P on the terminal side of angle $\alpha$ is P$(x, \sqrt{5})$, with $\cos\alpha = \frac{\sqrt{2}}{4}x$, find the values of $\sin\alpha$ and $\tan\alpha$;  
(2) It is known that there is a point P$(x, -1)$ ($x \neq 0$) on the terminal side of angle $\theta$, and $\tan\theta = -x$, find $\sin\theta$ and $\cos\theta$.

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