
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 $\triangle ABC$, the three internal angles are $A$, $B$, and $C$. If $\dfrac{\sqrt{3}\cos A + \sin A}{\sqrt{3}\sin A - \cos A} = \tan(-\dfrac{7}{12}\pi)$, find the maximum value of $2\cos B + \sin 2C$.

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