
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 an arithmetic sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$. The sequence satisfies the conditions $a\_1=1$ and $S\_9=81$.

(1) Find the general term formula for $\{a\_n\}$;

(2) Calculate the value of $\frac{1}{S\_1+1} + \frac{1}{S\_2+2} + ... + \frac{1}{S\_{2017}+2017}$.

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