
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
Define ${A}_{x}^{m}=x\left(x-1\right)\ldots \left(x-m+1\right)$, where $x\in R$, $m$ is a positive integer, and ${A}_{x}^{0}=1$. This is a generalization of the permutation number ${A}_{n}^{m}$ ($n$ and $m$ are positive integers, and $m\leqslant n$).  
$(1)$ Find the value of ${A}_{-15}^{3}$;  
$(2)$ Determine the monotonic intervals of the function $f\left(x\right)={A}_{x}^{3}$.

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