
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
In the Cartesian coordinate system, the vertex of angle $\alpha$ is at the origin of the coordinates, and the initial side coincides with the non-negative x-axis. After rotating the terminal side of angle $\alpha$ counterclockwise by $\frac{π}{6}$, the terminal side of the resulting angle intersects the unit circle with the center at the origin of the coordinates at point $P({-\frac{3}{5},\frac{4}{5}})$. Find $sin({2α-\frac{π}{6}})$.

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