
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
In the arithmetic sequence $\{a_n\}$, with a common difference $d \neq 0$, $a_2$ is the geometric mean of $a_1$ and $a_4$. It is known that the sequence $a_1$, $a_3$, $a_{k_1}$, $a_{k_2}$, …, $a_{k_n}$, … forms a geometric sequence. Find the general term $k_n$ of the sequence $\{k_n\}$.

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