
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 sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and they satisfy $(2a-c)\cos B=b\cos C$.

(1) Find the measure of angle $B$.

(2) Given vectors $\vec{m}=(\sin A,\cos 2A)$ and $\vec{n}=(6,1)$, find the maximum value of $\vec{m}\cdot \vec{n}$.

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