
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 a four-digit natural number $A$, if the digit in the thousands place is $5$ more than the digit in the tens place, and the digit in the hundreds place is $3$ more than the digit in the units place, then $A$ is called a "five-three number." For example, for the four-digit number $6714$, since $6-1=5$ and $7-4=3$, therefore $6714$ is a "five-three number"; for the four-digit number $8821$, since $8-2\neq 5$, therefore $8421$ is not a "five-three number". The difference between the largest and smallest "five-three numbers" is ______; for a "five-three number" $A$ with the digit in the thousands place being $a$, the digit in the hundreds place being $b$, the digit in the tens place being $c$, and the digit in the units place being $d$, let $M(A)=a+c+2(b+d)$ and $N(A)=b-3$. If $\frac{M(A)}{N(A)}$ is divisible by $5$, then the value of $A$ that satisfies the condition is ______.

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