
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 $f(x)=\dfrac{ax^{2}}{2}-(1+2a)x+2\ln x$, where $a > 0$, find the range of $a$ such that $f(x)$ has a maximum value in the interval $\left(\dfrac{1}{2},1\right)$.

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