
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
Let the function $f(x)=4\ln x+ax^{2}+bx$ ($a,b\in\mathbb{R}$), and $f'(x)$ be the derivative of $f(x)$, with $1$ and $4$ being the two extreme points of $f(x)$.  
$(1)$ Find the expression of $f(x)$;  
$(2)$ If $f(x)$ is monotonically decreasing in the interval $(2m, m+1)$, find the range of the real number $m$.

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