
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
If for the geometric sequence $\{a_n\}$ the product of its first $n$ terms is denoted by $T_n$, then it holds that $$T_{3n}=\left( \frac {T_{2n}}{T_{n}}\right)^{3}$$; by analogy, the following correct conclusion can be drawn: If for an arithmetic sequence the sum of its first $n$ terms is denoted by $S_n$, then the relationship is _______.

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