
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
(1) Find the range of real number $a$ such that for any real number $x$, $|x-1|+|x-3| \geqslant a^{2}+a$ always holds;
(2) If $a+b=1$, find the minimum value of $\dfrac {1}{4|b|}+ \dfrac {|b|}{a}$, and specify the value of $a$ when the minimum value is attained;
(3) Find the range of $y=\dfrac {2a}{a^{2}+1}$, where $a \in [2,+\infty)$.

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