
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 $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively, and $2b\cos C=2a+c$.
1. Find the measure of angle $B$;
2. If $2\sqrt{3}\sin \left(\dfrac{A}{2}+\dfrac{\pi }{6}\right)\cos \left(\dfrac{A}{2}+\dfrac{\pi }{6}\right)-2\sin ^{2}\left(\dfrac{A}{2}+\dfrac{\pi }{6}\right)=\dfrac{11}{13}$, find the value of $\cos C$.

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