
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. If for any real number $x$, the inequality $|x-1|+|x-3|\geq a^2+a$ always holds, find the range of the real number $a$.
2. If $a+b=1$, find the minimum value of $\frac {1}{4|b|}+ \frac {|b|}{a}$, and determine the value of $a$ when this minimum is attained.
3. Find the range of values for $y= \frac {2a}{a^{2}+1}$, where $a\in[2,+\infty)$.

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