
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 sinα + cosα = $\frac{2}{3}$.

1. Find the value of sin($\frac{3π}{2}-α$)cos($-\frac{π}{2}-α$).
2. If α is an angle in the second quadrant and the terminal side of angle β lies on y = 2x, find the value of $\frac{1}{sin(π - α)} - \frac{1}{cos(2π - α)} + \frac{sinθ - cosθ}{2sinθ + cosθ}$.

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