
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 sequence $\{a\_n\}$ with the first term $a\_1= \frac {3}{2}$, the sum of the first $n$ terms is $S\_n$, and it satisfies $2a_{n+1}+S_{n}=3$ ($n∈N^{*}$). Find the sum of all $n$ that satisfy $\frac {18}{17} < \frac {S_{2n}}{S_{n}} < \frac {8}{7}$.

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