
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 $f(x)=2\ln x+\frac{a}{{x}^{2}}$.  
$(1)$ If the tangent line of $f(x)$ at $(1,f(1))$ is parallel to the x-axis, find the value of $a$.  
$(2)$ Determine if $f(x)$ has any extreme points. If it does, find the extreme points; if not, explain why.  
$(3)$ If $f(x)=2$ has two solutions in the interval $[1,+\infty)$, find the range of values for $a$.

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