
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 the function $f(x) = \frac{x}{3x+1}$, the sequence $\{a_n\}$ has its first term equal to 1 and its common ratio equal to $f(1)$; the sequence $\{b_n\}$ has its first term $b_1 = \frac{1}{3}$, satisfying the recursive relation $b_{n+1} = f(b_n)$.  
(Ⅰ) Find the general formula for the sequences $\{a_n\}$ and $\{b_n\}$.  
(Ⅱ) Let $c_n = \frac{a_n}{b_n}$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, denoted as $T_n$.

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