
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 an arithmetic sequence $\{a\_n\}$ with a non-zero common difference, some terms of the sequence ($a_{k_1}, a_{k_2}, a_{k_3}, \ldots$) form a geometric sequence $\{a_{k_n}\}$. If $k_1 = 1$, $k_2 = 2$, and $k_3 = 6$, find the value of $k_4$.
A) 20
B) 22
C) 24
D) 28

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