
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 $\{a_n\}$ whose sum of the first n terms $S_n = 2a_n - 2^{n+1}$, if the inequality $2n^2 - n - 3 < (5 - \lambda)a_n$ always holds for any $n \in \mathbb{N}^+$, then the maximum value of the integer $\lambda$ is ______.

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