
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 $0<β<α<\frac{π}{2}$, point $P(1, 4\sqrt{3})$ lies on the terminal side of angle $α$, and $\sinα\sin(\frac{π}{2}-β)+\cosα\cos(\frac{π}{2}+β)=\frac{3\sqrt{3}}{14}$, find the value of angle $β$.

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