
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 $\{a_n\}$ whose sum of the first $n$ terms is $S_n$, and a geometric sequence $\{b_n\}$ whose sum of the first $n$ terms is $T_n$, satisfying $a_1 = b_1$, $2a_2 = b_2$, $S_2 + T_2 = 13$, and $2S_3 = b_3$.  
(I) Find the general formula for the sequences $\{a_n\}$ and $\{b_n\}$.  
(II) Let $c_n = \frac{2a_n}{b_n}$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, denoted as $C_n$.

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