
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
Suppose a sequence $\{a\_n\}$ satisfies $a\_2-a\_1 > a\_3-a\_2 > a\_4-a\_3 > … > a\_{n+1}-a\_n > …$, then the sequence $\{a\_n\}$ is called a "difference decreasing" sequence. If sequence $\{a\_n\}$ is a "difference decreasing" sequence, and its general term $a\_n$ and the sum of its first $n$ terms $S\_n (n∈N^{})$ satisfy $2S\_n=3a\_n+2λ-1 (n∈N^{})$, then the range of the real number $λ$ is _____ .

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