
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
A new operation ※ is defined between two non-zero numbers $a$ and $b$ as follows: if $a^{c}=b$, then $a$※$b=c$. For example, since $5^{2}=25$, then $5$※$25=2$, and since $5^{0}=1$, then $5$※$1=0$.  
$(1)$ According to the above definition, fill in the blanks: $2$※$8=$______; $2$※$\frac{1}{16}=$______.  
$(2)$ If $x$※$\frac{1}{16}=2$, then $x=$______.  
$(3)$ During the operation, according to the above definition: let $4$※$5=x$, $4$※$6=y$, please explain why the following equation holds: $4$※$5+4$※$6=4$※$30$.

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