
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 $0 < α < π$ and $0 < β < π$, and the equations $\cos(\frac{π}{2}-α) = \sqrt{2}\cos(\frac{3π}{2}+β)$ and $\sqrt{3}\sin(\frac{3π}{2}-α) = -\sqrt{2}\sin(\frac{π}{2}+β)$ hold, find the values of $α$ and $β$.

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