
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 $f(x)= \frac{2x^{2}}{x+1}$ and $g(x)=a\sin \frac{πx}{2}+5-2a (a > 0)$, if for any $x\_1\in[0,1]$, there always exists $x\_0\in[0,1]$ such that $g(x\_0)=f(x\_1)$ holds, then the range of values for $a$ is _______.

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