
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 sequence $\{a_n\}$ that satisfies $a_n = \frac{kn-3}{n-\frac{3}{2}}$ (where $k$ is a constant).  
(1) If the sequence $\{a_n\}$ is an arithmetic sequence, find the value of $k$;  
(2) If $k \neq 2$, find the maximum and minimum terms of the sequence $\{a_n\}$;  
(3) If $a_n > \frac{k2^n+(-1)^n}{2^n}$ for any $n \in \mathbb{N}^*$ always holds, find the range of $k$.

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