
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) Find the value of $\frac{2\sqrt{2}\sin{\alpha} + 3\sin{\left( \frac{\pi}{2} + \alpha \right)}}{\cos{\left( \pi + \alpha \right)} + \sqrt{2}\cos{\left( \frac{5\pi}{2} + \alpha \right)}}$

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