
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 circle $x^2+y^2=3$ at point P in the first quadrant, where P has coordinates $(m, \sqrt{2})$, find:  
(1) The value of $\tan\alpha$;  
(2) The value of $\frac{2\cos^2\frac{\alpha}{2}-\sin\alpha-1}{\sqrt{2}\sin\left(\frac{\pi}{4}+\alpha\right)}$.

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