
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 the sets $M=\\left\\{ \\left. x\\left| \\left. m\\leqslant x\\leqslant m+ \\dfrac{3}{4} \\right. \\right. \\right. \\right\\}$ and $N=\\left\\{ \\left. x\\left| \\left. n- \\dfrac{1}{3}\\leqslant x\\leqslant n \\right. \\right. \\right. \\right\\}$, where both $M$ and $N$ are subsets of the set $\{x|0\\leqslant x\\leqslant 1\}$. If we define the "length" of a set $\{x|a\\leqslant x\\leqslant b\}$ as $(b-a)$, what is the minimum "length" of the set $M\\cap N$?

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