
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
If the sequence $\{a_n\}$ satisfies $a_2 - a_1 > a_3 - a_2 > a_4 - a_3 > \ldots > a_{n+1} - a_n > \ldots$, then the sequence $\{a_n\}$ is called a "decreasing difference" sequence. If the sequence $\{a_n\}$ is a "decreasing difference" sequence, and its general term $a_n$ and the sum of its first $n$ terms $S_n$ ($n \in \mathbb{N}^*$) satisfy $2S_n = 3a_n + 2\lambda - 1$ ($n \in \mathbb{N}^*$), then the range of the real number $\lambda$ is \_\_\_\_\_\_.

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