
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 $\alpha$ passes through point $P(m,2\sqrt{2})$, $\sin{\alpha}=\frac{2\sqrt{2}}{3}$, and $\alpha$ is in the second quadrant.

(1) Find the value of $m$;

(2) If $\tan{\beta}=\sqrt{2}$, find the value of $\frac{\sin{\alpha}\cos{\beta}+3\sin(\frac{\pi}{2}+\alpha)\sin{\beta}}{\cos(\pi+\alpha)\cos(-\beta)-3\sin{\alpha}\sin{\beta}}$.

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