
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
(1) Find the maximum value of the function $f(x)=2\cos x+\sin x$.
(2) Given that the function $f(x)$ is an odd function defined on $R$, and $f(x)=2x^{3}+x^{2}$ when $x∈(-∞,0)$, find $f(2)$.
(3) The length, width, and height of a rectangular box are 3, 2, and 1 respectively, and all its vertices are on the surface of sphere $O$. Find the surface area of sphere $O$.
(4) In $ΔABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $2b\cos B=a\cos C+c\cos A$, find $B$.

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