
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 $0 < \beta < \alpha < \frac{\pi}{2}$, point $P(1,4 \sqrt{3})$ is a point on the terminal side of angle $\alpha$, and $\sin \alpha \sin \left(\frac{\pi}{2}-\beta \right)+\cos \alpha \cos \left(\frac{\pi}{2}+\beta \right)= \frac{3 \sqrt{3}}{14}$, calculate the value of angle $\beta$.

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