
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
In the Cartesian plane with the coordinate system $xoy$, if the initial side of angle $\alpha$ is the non-negative half of the $x$-axis and its terminal side passes through point $P(2,4)$.

1. Find the value of $\tan \alpha$;
2. Find the value of $\frac{2\sin (\pi-\alpha)+2\cos ^{2} \frac{\alpha}{2}-1}{ \sqrt{2}\sin (\alpha+ \frac{\pi}{4})}$.

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