
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 the function $f(x)=|x-a|+|x+b|$ where $(a > 0,b > 0)$.  
(I) If $a=1$, $b=2$, solve the inequality $f(x) \leqslant 5$;  
(II) If the minimum value of $f(x)$ is $3$, find the minimum value of $\dfrac {a^{2}}{b}+ \dfrac {b^{2}}{a}$.

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