
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 $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively, and it is given that $(2a-c)\cos B = b\cos C$;  
(1) Find the magnitude of angle $B$;  
(2) Let $\overrightarrow{m} = (\sin A, \cos 2A)$, $\overrightarrow{n} = (4k, 1)$ (where $k > 1$), and the maximum value of $\overrightarrow{m} \cdot \overrightarrow{n}$ is 5, find the value of $k$.

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