
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 that the sum of the first n terms ($S_n$) of the sequence ${a_n}$ satisfies $\sqrt {S_{n}} = \sqrt {S_{n-1}} + 1$ (for $n \geq 2, n \in \mathbb{N}$) and $a_1 = 1$.
(1) Find the general term (${a_n}$) of the sequence;
(2) Denote $b_n = \frac{1}{a_n \cdot a_{n+1}}$, and $T_n$ is the sum of the first n terms of ${b_n}$. Find the minimum value of n for which $T_n \geq \frac{2}{n}$.

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