
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 function
$$
f(x) = \frac{(k+1) x^{2} + (k+3) x + (2 k-8)}{(2 k-1) x^{2} + (k+1) x + (k-4)},
$$

find the set of real numbers \( k \) for which \( f(x) > 0 \) for any \( x \in D \), where \( D \) is the domain of \( f(x) \).

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