
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 sum of the first $n$ terms of an arithmetic sequence $\{a\_n\}$ is $S\_n$, and $S_6 = 5S_2 + 18$, $a_{3n} = 3a_n$. The sequence $\{b_n\}$ satisfies $b_1 \cdot b_2 \cdot \ldots \cdot b_n = 4^{S_n}$.
(I) Find the general term formulas for the sequences $\{a_n\}$ and $\{b_n\}$;
(II) Let $c_n = \log_2 b_n$, and the sum of the first $n$ terms of the sequence $\{\frac{1}{c_n \cdot c_{n+1}}\}$ is $T_n$, find $T_{2016}$.

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