
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
The sequence $\{a_n\}$ satisfies $a_{n+1} - a_n = 2$, $a_1 = 2$, and the geometric sequence $\{b_n\}$ satisfies $b_1 = a_1$, $b_4 = a_8$.
(I) Find the general term formula for the sequences $\{a_n\}$ and $\{b_n\}$;
(II) Let $c_n = a_n b_n$, find the sum of the first $n$ terms $T_n$ for the sequence $\{c_n\}$.

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