
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 vertex of angle $\alpha$ is at the origin, its initial side coincides with the non-negative half of the $x$-axis, and its terminal side intersects the unit circle at point $P(-\frac{3}{5}, \frac{4}{5})$,
(1) Find $\sin \alpha$
(2) Find the value of $\frac{\sin 2\alpha + \cos 2\alpha + 1}{1 + \tan \alpha}$.

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