
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 power function $f(x)=x^{k^{2}-2k-3}(k\in\mathbb{N}^{*})$ whose graph is symmetric about the $y$-axis and is a decreasing function in the interval $(0,+\infty)$,  
$(1)$ find the analytical expression of the function $f(x)$;  
$(2)$ if $a > k$, compare the size of $(\ln a)^{0.7}$ and $(\ln a)^{0.6}$.

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