
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 ($S_n$) of a sequence of positive numbers ${{a_n}}$ satisfies ${a_1} = 1$ and $S_n = n^2$, find:

(I) The general term formula for the sequence ${{a_n}}$;

(II) If ${b_n} = \frac{1}{{{a_n} \cdot {a_{n + 1}}}}$, denote the sum of the first $n$ terms of the sequence ${{b_n}}$ as ${T_n}$. Find ${T_n}$.

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