
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 $β$ is an angle in the second quadrant and satisfies the equation $\frac{2\tan^{2}{β}}{3\tan{β} + 2} = 1$, find:
1. $\sin(β + \frac{3π}{2})$
2. $\frac{2}{3}\sin^{2}{β} + \cos{β} \cdot \sin{β}$.

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