
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 functions $f(x)= \frac {1}{2}ax^{2}-(2a+1)x+2\ln x(a∈R).g(x)=x^{2}-2x$, if for any $x\_1∈(0,2]$, there exists $x\_2∈(0,2]$, such that $f(x\_1) < g(x\_2)$, then the range of values for $a$ is _____ .

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