
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 $f(x)= \begin{cases} \frac{1}{4^{x}},x\in[0, \frac{1}{2}] \\ -x+1,x\in( \frac{1}{2},1] \end{cases}$ and $g(x)=a\sin ( \frac{π}{6}x)-a+2(a > 0)$, if there exists $x_{1}$ and $x_{2}\in[0,1]$ 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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