
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 $\cos\left( \frac{\pi}{2} - \alpha \right) = \sqrt{2} \cos\left( \frac{3\pi}{2} + \beta \right)$ and $\sqrt{3} \sin\left( \frac{3\pi}{2} - \alpha \right) = - \sqrt{2} \sin\left( \frac{\pi}{2} + \beta \right)$, with $0 < \alpha < \pi$ and $0 < \beta < \pi$, find the values of $\alpha$ and $\beta$.

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