
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 geometric sequence $\{a_n\}$ with a common ratio $q$ and the first term $a_1 < 0$, the sum of the first $n$ terms is $S_n$. Suppose $a_1$, $a_4$, $a_3-a_1$ form an arithmetic sequence. If $S_k < 5S_{k-4}$, then the maximum value of the positive integer $k$ is $\boxed{\text{(A) } 4}$.

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