
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 $f(x)=ax^{2}-\ln x$, where $a\in \mathbb{R}$.  
(I) When $a=1$, find the equation of the tangent line to the function $f(x)$ at the point $(1,f(1))$.  
(II) Determine whether there exists a real number $a$ such that the minimum value of the function $f(x)$ on the interval $(0,e]$ is $\frac{3}{2}$. If it exists, find the value of $a$; if not, explain why.

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