
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 a sequence $\{a\_n\}$ where all terms are positive, let $S\_n$ denote the sum of its first $n$ terms. It is known that $a\_1=1$, and $(S_{n+1}+λ)a\_n=(S\_n+1)a_{n+1}$ holds for all $n∈\mathbb{N}^*$.

1. Find the values of $a\_2$ and $a\_3$.
2. Find the value of $λ$ such that the sequence $\{a\_n\}$ is an arithmetic sequence.
3. If $λ=1$, find the general formula for the sequence $\{a\_n\}$.

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