
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 $f(x)= \begin{cases} -\frac{1}{2}x+\frac{1}{4},x\in[0,\frac{1}{2}] \\ \frac{2x^{2}}{x+2},x\in(\frac{1}{2},1]\\ \end{cases},g(x)=a\cos\frac{\pi x}{2}+5-2a (a>0)$, if for any $x_{1}\in[0,1]$, there always exists $x_{2}\in[0,1]$, such that $f(x_{1})=g(x_{2})$ holds true, then the range of the real number $a$ is \_\_\_\_\_\_.

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