
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 $\overrightarrow {OA} = (1, 0)$, $\overrightarrow {OB} = (1, 1)$, and $(x, y) = \lambda \overrightarrow {OA} + \mu \overrightarrow {OB}$, if $0 \leq \lambda \leq 1 \leq \mu \leq 2$, and $z = \frac {x}{m} + \frac {y}{n}$ ($m > 0$, $n > 0$) has a maximum value of 2, then the minimum value of $m+n$ is \_\_\_\_\_\_.

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