
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 $S_{n}$ is the sum of the first $n$ terms of the sequence ${a_{n}}$, and $S_{n}=n^{2}-4n+4$.
(1) Find the general term formula of the sequence ${a_{n}}$;
(2) Let ${c_{n}}$ be a sequence where all $c_{n}$ are non-zero, and the number of positive integers $k$ satisfying $c_{k}⋅c_{k+1} < 0$ is called the signum change number of this sequence. If $c_{n}=1- \frac {4}{a_{n}}$ ($n$ is a positive integer), find the signum change number of the sequence ${c_{n}}$;
(3) Let $T_{n}$ be the sum of the first $n$ terms of the sequence ${\frac {1}{a_{n}}}$. If $T_{2n+1}-T_{n}\leqslant \frac {m}{15}$ holds for all positive integers $n$, find the minimum value of the positive integer $m$.

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