
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
Points $A$ and $B$ are located on the unit circle $O$. Point $A$ intersects with the positive semi-axis of the $x$-axis, while point $B$ is in the second quadrant. Denote $\angle AOB = \theta$ and $\sin \theta = \frac{4}{5}$.

1. Find the coordinates of point $B$.
2. Calculate the value of $\frac{\sin (\pi + \theta) + 2 \sin (\frac{\pi}{2} - \theta)}{2 \cos (\pi - \theta)}$.

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