
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
Let $\{a_n\}$ be a sequence with a sum of first $n$ terms represented as $S_n = 2n^2$. Let $\{b_n\}$ be a constant sequence, and it is given that $a_1 = b_1$ and $b_{-1} = b_1$. Define the sequence $\{c_n\}$ by $c_n = \frac{a_n}{b_n}$. Find the sum of the first $n$ terms of the sequence $\{c_n\}$.

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