
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 inequality about $x$ $(4kx-k^2-12k-9)(2x-11)>0$, where $k \in \mathbb{R}$, for the solution set $A$ of the inequality, let $B=A \cap \mathbb{Z}$ (where $\mathbb{Z}$ is the set of integers). If set $B$ is finite, then the range of real numbers $k$ that makes the number of elements in set $B$ the smallest is \_\_\_\_\_\_.

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