
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 $b$, define the operation: $a▲b= \begin{cases} a^{b} & (a > b, a \neq 0) \\ a^{-b} & (a \leqslant b, a \neq 0) \end{cases}$;  
For example: $2▲3=2^{-3}= \dfrac {1}{8}$, $4▲2=4^{2}=16.$ Calculate $\[2▲(-4)\]×\[(-4)▲(-2)\]$ according to this definition of operation.

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