
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 its first $n$ terms sum $S_n$, and it satisfies $S_n + 2 = 2a_n$, $n \in \mathbb{N}^*$.
(1) Find the general term formula of the sequence ${a_n}$.
(2) Let $b_n = \frac{1}{\log_2 a_n}$ and $c_n = \frac{\sqrt{b_n b_{n+1}}}{\sqrt{n+1} + \sqrt{n}}$, 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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