
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 recursive sequence $\left\{x_{n}\right\}$ that satisfies $x_{n+1}=x_{n}^{2}-4x_{n}$ for $n=1, 2, \cdots$, if for any initial term $x_{1} \in \mathbf{R}$ such that $x_{1} \neq 0$, there is always a term $x_{k} \geqslant b$ in the sequence, then the largest integer not exceeding $(2b-3)^{2}$ is ______.

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