
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 $\{a_n\}$ where the first term $a_1 = 1$, the common difference $d > 0$, and the second, fifth, and fourteenth terms respectively correspond to the second, third, and fourth terms of a geometric sequence $\{b_n\}$:

1. Find the general formulas for the sequences $\{a_n\}$ and $\{b_n\}$;
2. Let there be a sequence $\{c_n\}$ such that for $n \in \mathbb{N}^*$, the following equation holds: 
$$
\frac{c_1}{b_1} + \frac{c_2}{b_2} + \ldots + \frac{c_n}{b_n} = a_{n+1}.
$$
Find the sum of the first 2016 terms of $\{c_n\}$: $c_1 + c_2 + c_3 + \ldots + c_{2016}$.

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