
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
Let $f(x)= \dfrac {a}{x}+x^2$ and $g(x)=x^3-x^2-3$.  
If for any $s$, $t \in \left[ \dfrac {1}{2}, 2 \right]$, it holds that $f(s) \geqslant g(t)$, find the range of real numbers $a$.

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