
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 $f(x)= \begin{cases}\frac {2x^{2}}{x+1},x\in( \frac {1}{2},1] \\ - \frac {1}{3}x+ \frac {1}{6},x\in[0, \frac {1}{2}]\end{cases},g(x)= \frac {1}{2}ax^{2}-2a+2(a > 0)$, if there exists $x_{1}$, $x_{2}\in[0,1]$, such that $f(x_{1})=g(x_{2})$ holds, then the range of values for the real number $a$ is \_\_\_\_\_\_.

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