
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 the curve $y=f\left(x\right)$ at the point $\left(1,f\left(1\right)\right)$ is parallel to the x-axis, find the value of the real number $a$.  
$(2)$ If $f\left(x\right)$ is a decreasing function on the interval $\left[1,3\right]$, find the range of values for the real number $a$.

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