
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 that the first term of the geometric sequence $\{a_n\}$ is $1$ and the common ratio is $3$, and the first term of the arithmetic sequence $\{b_n\}$ is $-5$ and the common difference is $1$. The terms of $\{b_n\}$ are successively inserted between every two adjacent terms of $\{a_n\}$ to form a new sequence $\{c_n\}$ according to the following rule: $a_1$, $b_1$, $a_2$, $b_2$, $b_3$, $a_3$, $b_4$, $b_5$, $b_6$, $a_4$, ..., that is, successively insert $n$ terms from $\{b_n\}$ between $a_n$ and $a_{n+1}$. Then find the value of $c_{2018}$.

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