
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 of a sequence of positive numbers ${a_{n}}$ is $S_{n}$, and for all $n∈N^{*}$, $2S_{n}=a_{n}^{2}+a_{n}$. Let $b_{n}= \dfrac {1}{a_{n} \sqrt {a_{n+1}}+a_{n+1} \sqrt {a_{n}}}$, and the sum of the first $n$ terms of ${b_{n}}$ is $T_{n}$. The number of rational numbers in $T_{1}$, $T_{2}$, $T_{3}$, $…$, $T_{100}$ is \_\_\_\_\_\_.

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