
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 $\{a\_n\}$ that satisfies $a\_1=a$, $2a\_n-a_{n+1}=n-1$, and $b\_n=a\_n-n$.
(1) Determine whether the sequence $\{b\_n\}$ is a geometric sequence and explain the reason.
(2) If $a=2$, find the sum $S\_n$ of the first $n$ terms of the sequence $\{a\_n\}$.

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