
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 $a\_1=1$, $a\_2=2$, and the sum of the first $n$ terms denoted by $S\_n$. It is known that $(S\_{n+2}-S\_{n+1})-2(S\_{n+1}-S\_{n})=2$, for all $n∈N^{*}$. Find the general term $a\_n=$ \_\_\_\_\_\_.

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