
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 $f(x)=\ln x+x^{2}-2ax+a^{2}$, where $a\in\mathbb{R}$.

1. If $a=0$, find the minimum value of the function $f(x)$ on the interval $[1,e]$.
2. If the function $f(x)$ has a monotonically increasing interval on $[\frac{1}{2},2]$, find the range of values for the real number $a$.
3. Discuss the extreme value points of the function $f(x)$ based on different values of $a$.

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