
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 \lt \alpha\ \ \lt \beta\ \ \lt 2\pi $, and the function $f\left(x\right)=5\sin (x-\frac{\pi}{6})$. If $f\left(\alpha \right)=f\left(\beta \right)=1$, then $\cos \left(\beta -\alpha\right)$.

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