
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 material and solve the following problems: Dynamic number: a four-digit positive integer, with each digit not being $0$, combine the digit in the thousandth place and the hundredth place to form a two-digit number, and combine the digit in the tenth place and the unit place to form a two-digit number. If the two-digit number formed by the digit in the tenth place and the unit place is twice the two-digit number formed by the digit in the thousandth place and the hundredth place, then this four-digit positive integer is called a "dynamic number." For example, the four-digit number $2346$, the two-digit number formed by the digit in the thousandth place and the hundredth place is $23$, and the two-digit number formed by the digit in the tenth place and the unit place is $46$. Since $46=2\times 23$, $2346$ is a "dynamic number." We can use these two two-digit numbers to represent the "dynamic number," such as $2346$ can be represented as: $23\times 100+46$.  
$(1)$ Determine whether $3470$ is a "dynamic number," and explain the reason;  
$(2)$ Please write down a "dynamic number": ______, and use the two-digit number formed by its thousandth place and hundredth place, and the two-digit number formed by its tenth place and unit place to represent this "dynamic number": ______;  
$(3)$ If $a$ represents a "dynamic number" formed by the two-digit number in the thousandth place and the hundredth place, then this "dynamic number" can be represented as ______; (expressed in an algebraic expression containing $a$)  
$(4)$ Swap the two-digit number formed by the thousandth place and the hundredth place and the two-digit number formed by the tenth place and the unit place of the "dynamic number" in (3) to obtain a new four-digit number. Bright Liang found that the sum of the original "dynamic number" and the new four-digit number must be a multiple of $3$. Please help Liang explain the reason.

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