
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
Read the following material:<br/>If two numbers $a$ and $b$ satisfy $a^{x}=b$, then $x$ is called the "logarithm" of $b$ with respect to $a$, denoted as $\left(a,b\right)=x$, such as $4^{2}=16$, so $\left(4,16\right)=2$.<br/>According to the above rules, answer the following questions:<br/>$(1)$ According to the above rules, please fill in the blanks:<br/>$(3,27)=\_\_\_\_\_\_,\left(-2,16\right)=\_\_\_\_\_\_$,$(-\frac{2}{3},\_\_\_\_\_\_)=3.$<br/>$(2)$ Calculate $\left(3,2\right)+\left(3,4\right)=( \_\_\_\_\_\_,\_\_\_\_\_\_)$, and write down the calculation process;<br/>$(3)$ Write down the results directly:<br/>①$\left(5,10\right)-\left(5,2\right)=$______；<br/>②$\left(10,4\right)\times \left(2,10\right)=\_\_\_\_\_\_.$

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