
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 $f(x)= \dfrac {4x}{3x^{2}+3}$ and the function $g(x)= \dfrac {1}{3}ax^{3}-a^{2}x$ (where $a\neq 0$), determine the range of the real number $a$ such that for any $x_{1}\in [0,2]$, there exists an $x_{2}\in [0,2]$ such that $f(x_{1})=g(x_{2})$.

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