
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 two sequences $\{a_n\}$ and $\{b_n\}$, satisfying $a_1=b_1=3$, $a_{n+1}-a_n= \frac {b_{n+1}}{b_n}=3$, $n\in\mathbb{N}^*$, if sequence $\{c_n\}$ satisfies $c_n=b_{a_n}$, calculate the value of $c_{2013}$.

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