
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 ${S_n}$ be the sum of the first $n$ terms of the sequence ${a_n}$. If $\frac{S_{2n}}{S_n} (n \in \mathbb{N^*})$ is a non-zero constant, then the sequence ${a_n}$ is called a "sum-geometric sequence". If the sequence ${c_n}$ is an arithmetic sequence with first term ${c_1}$ and common difference $d (d \neq 0)$, and the sequence ${c_n}$ is a "sum-geometric sequence", denote $d = f({c_1})$. Find $f(2018)$ =______.

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