
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 four-digit natural number $M$, if the digits in each place are all non-zero and the digit in the unit place is greater than $1$, and satisfies that the sum of the digits in the hundreds place and the tens place is three times the sum of the digits in the thousands place and the unit place, then this four-digit number $M$ is called a "triple-three number". For example, $M=1843$, since $8+4=3\times \left(1+3\right)$, therefore 1843 is a "triple-three number"; if the sum of the digits of a "triple-three number" $M$ is $16$, and it is specified: by exchanging the tens and hundreds digits of this "triple-three number" $M$ to get ${M'}$, let $G(M)=|\frac{M-{M'}}{270}|$, and let the absolute difference between the digit in the thousands place and the digit in the unit place of $M$ be denoted as $Q\left(M\right)$. If $\frac{G(M)}{Q(M)}$ is a positive integer, then all the values of $M$ that satisfy the conditions are ______.

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