
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 follows: $a*b=\left\{\begin{array}{l}{{a}^{b} \text{ when } a>b \text{ and } a\neq 0}\\{{a}^{-b} \text{ when } a<b \text{ and } a\neq 0}\end{array}\right.$. For example, $2*3=2^{-3}=\frac{1}{8}$. Calculate: $\left[2*\left(-4\right)\right]\times \left[\left(-4\right)*\left(-2\right)\right]=$____.

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