
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
(1) In the sequence $\{a\_n\}$, $S\_n$ is the sum of its first $n$ terms. Given that $S\_n=2n^{2}-3n+2$; find the general term $a\_n$.
(2) The sequence $\{a\_n\}$ satisfies: $a\_1=1$, $a_{n+1}=a_{n}+n$, $n∈\mathbb{N}^{*}$. Find the general term $a\_n$.

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