
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 $\triangle ABC$, it is known that $\sin \left(A+ \dfrac{\pi}{6}\right)=2\cos \left(A\right)$.

$(1)$ Find $\tan A$;

$(2)$ If $B\in\left(0, \dfrac{\pi}{3}\right)$ and $\sin \left(A-B\right)= \dfrac{3}{5}$, find $\sin B$.

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