
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 $\{a\_n\}$, the sum of its first $n$ terms is $S\_n= \frac{3}{2}n^{2}- \frac{1}{2}n$.
1. Find the general term formula $a\_n$;
2. When $n\geqslant 2$, the inequality $a\_{n+1}+ \frac{λ}{a\_n}\geqslant λ$ always holds true, find the range of the real number $λ$.

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