
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: $a\_1=1$, $na_{n+1}-(n+1)a_{n}=1(n∈N_{+})$
(1) Find the general term formula of the sequence $\{a\_n\}$;
(2) If $b_{n}= \frac {a_{n}+1}{2}\cdot ( \frac {8}{9})^{n}(n∈N_{+})$, find the maximum term of the sequence $\{b_{n}\}$.

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