
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
Given that $\overrightarrow{OA}=(1,0)$, $\overrightarrow{OB}=(1,1)$, and $(x,y)=λ \overrightarrow{OA}+μ \overrightarrow{OB}$, if $0\leqslant λ\leqslant 1\leqslant μ\leqslant 2$, then the maximum value of $z= \frac {x}{m}+ \frac{y}{n}(m > 0,n > 0)$ is $2$. Find the minimum value of $m+n$.

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