
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 $(kx-k^{2}-4)(x-4) > 0$, where $k\in\mathbb{R}$.
(1) Find the solution to the inequality;
(2) Does there exist a real number $k$ such that the solution set $A$ of the inequality contains only finitely many integers? If so, find the value of $k$ that minimizes the number of integers in $A$; if not, explain why.

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