
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
In the geometric sequence ${a_{n}}$, $a_{1}=2$, $a_{3}$, $a_{2}+a_{4}$, $a_{5}$ form an arithmetic sequence.
(1) Find the general term formula of the sequence ${a_{n}}$;
(2) If the sequence ${b_{n}}$ satisfies $b_{1}+ \frac {b_{2}}{2}+…+ \frac {b_{n}}{n}=a_{n}(n∈N^{})$ and the sum of the first $n$ terms of ${b_{n}}$ is $S_{n}$, find the maximum positive integer value of $n$ that makes $S_{n}-na_{n}+6\geqslant 0$ hold.

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