
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
Let $S_n$ and $T_n$ respectively denote the sum of the first $n$ terms of the sequences $\{a_n\}$ and $\{b_n\}$. It is known that for any $n \in \mathbb{N}^*$, the following holds: $3a_n = 2S_n + 3$. The sequence $\{b_n\}$ is an arithmetic sequence, and it is given that $T_5 = 25$, $b_{10} = 19$.

(I) Find the general formula for the sequences $\{a_n\}$ and $\{b_n\}$.
(II) Let $c_n = \frac {a_{n}b_{n}}{n(n+1)}$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, denoted as $R_n$.

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