
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 a sequence ${a_n}$ with the sum of its first $n$ terms denoted as $S_n, n \in \mathbb{N}^*$, and $S_n = \frac{3}{2}a_n - \frac{1}{2}$.
(1) Find the general formula for the sequence.
(2) If ${b_n} = \frac{2n}{a_{n+2} - a_{n+1}}$, let $T_n$ denote the sum of the first $n$ terms of the sequence ${b_n}, n \in \mathbb{N}^*$. If there exists a real number $k$ such that $T_n < k$, find the minimum value of $k$.

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