
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 $d$, some terms from $\{a_n\}$ form a geometric sequence, namely $a_{k_1}$, $a_{k_2}$, … $a_{k_n}$, where $k_1 = 1$, $k_2 = 5$, and $k_3 = 17$. Find:  
(1) The general term $k_n$;  
(2) The sum of the first n terms of the sequence $\{k_n\}$, denoted as $T_n$.

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