
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
Let $f(x)=\sin(x-\frac{π}{6})$. If for any $α∈[-\frac{{5π}}{6},-\frac{π}{2}]$, there exists a unique $\beta$ in the interval $\left[0,m\right]$ such that $f\left(\alpha \right)+f\left(\beta \right)=0$, then determine the minimum value of $m$.

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