
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 $\{ a_{n} \}$, $a_{1}=2$, and the sequence formed by $a_{3}$, $a_{2}+a_{4}$, $a_{5}$ is 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 true.

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