
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
For the problem "Given $x+y=1$, find the maximum value of $xy$", Xiao Ming solved it as follows:  
Since $x+y=1$, then $y=1-x$, so $xy=x(1-x)=x-x^{2}=-(x-\frac{1}{2})^{2}+\frac{1}{4}$;  
Therefore, $xy≤\frac{1}{4}$, so the maximum value of $xy$ is $\frac{1}{4}$.  
Please calculate using this method: when $2n+m=4$ ($m>0, n>0$), find the minimum value of $\frac{2}{m}+\frac{1}{n}$.

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