
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
For real numbers $a$ and $b$, the operation is defined as "$a*b=\left\{\begin{array}{l}{{a}^{2}-ab(a>b)}\\{ab-{b}^{2}(a\leq b)}\end{array}\right.$" For example, $4*2$, since $4 > 2$, then $4*2=4^{2}-4\times 2=8$. If $x_{1}$ and $x_{2}$ are the two roots of the quadratic equation $x^{2}-8x+16=0$, then $x_{1}*x_{2}=\_\_\_\_\_\_$.

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