
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 set $M={1,2,3,4,5,6}$, for $a\_i$, $b\_i∈M$, let $e_i= \frac {b\_i}{a\_i}$ with $a\_i < b\_i$. The set comprising all $e_i$ is denoted as $A={e\_1,e\_2,…e\_k}$.
(I) Find the value of $k$;
(II) Given the set $B={e’\_i|e’\_i= \frac {1}{e\_i},e\_i∈A}$, find the sum $\sum\limits_{i≠ j}e\_i-e’\_j$;
(III) Given $e\_i∈A$, $e’\_j∈B$, find the probability of $e\_i+e’\_j∈Z$.

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