
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 that the sum of the first $n$ terms of the arithmetic sequence $\{a\_n\}$ is $S\_n$, if the middle term of the arithmetic mean between $a\_2$ and $a\_{10}$ is $(-2)$, and $a\_1a\_6=14$

(I) Find the general term formula of the sequence $\{a\_n\}$;

(II) Let $f(n)= \frac {2S_{n}-2a_{n}}{n}(n∈N^{})$ , find the minimum value of $f(n)$ and the corresponding value of $n$.

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