
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 $\left(\frac{π}{3}, \frac{5π}{6}\right)$, and $\sin\left(α + \frac{π}{6}\right) = \frac{4}{5}$, $\cos\left(β - \frac{5π}{6}\right) = \frac{5}{13}$, find the value of $\sin\left(α - β\right)$.

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