
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
We define the "length" of a set $M={x|a≤x≤b}$ as $(b-a)$. If set $M={x|m≤x≤m+\frac{2}{3}}$, $N={x|n-0.5≤x≤n}$, and both sets $M$ and $N$ are subsets of ${x|0≤x≤1}$, then the minimum "length" of the set $M∩N$ is $\_\_\_\_\_\_$.

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