
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]


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Given that the sum of the first $n$ terms of the sequence ${a_n}$ is $S_n$, and $S_n = 2a_n - 2 (n \in \mathbb{N}^*)$, the sequence ${b_n}$ is such that $b_1 = 1$ and $b_{n+1} = \frac{b_n}{2b_n + 1} (n \in \mathbb{N}^*)$.

1. Find the general terms $a_n$ and $b_n$ of the sequences ${a_n}$ and ${b_n}$.
2. If $c_n = \frac{a_n}{b_n}$, find the sum of the first $n$ terms, $T_n$, of the sequence ${c_n}$.
3. If $h_n = \frac{a_n}{3^n \cdot b_n}$ and there exists a constant $\lambda$ such that $\lambda > h_n$ holds for all $n \in \mathbb{N}^*$, find the range of $\lambda$.

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