
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 $M={x|m\leqslant x\leqslant m+ \frac {3}{4}}$, $N={x|n- \frac {1}{3}\leqslant x\leqslant n}$, and $P={x|0\leqslant x\leqslant 1}$, where $M$ and $N$ are subsets of $P$. If we define the "length" of a set ${x|a\leqslant x\leqslant b}$ as $(b-a)$, determine the minimum "length" of the set $M\cap N$.

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