
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 $α$ and $β$ are in the interval $(0, \frac{π}{2})$ and satisfy the equation $\sin α \cos β - 2 \cos α \sin β = 0$, find the minimum value of $\tan (2π + α) + \tan (\frac{π}{2} - β)$.
A) $2$
B) $\sqrt{2}$
C) $1$
D) $2\sqrt{2}$

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