
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
If the difference between the hundreds digit and the thousands digit of a four-digit number $M$ is exactly twice the difference between the units digit and the tens digit, then this four-digit number $M$ is called a "Phoenix number." For example, $M=2456$, because $4-2=2\times \left(6-5\right)$, so $2456$ is a "Phoenix number." If the thousands digit of a "Phoenix number" is $a$, the hundreds digit is $b$, the tens digit is $c$, and the units digit is $d$, and it satisfies $\left(2\leqslant a\leqslant b \lt c\leqslant d\leqslant 9\right)$, let $G(M)=\frac{{49ac-2a+2d+23b-6}}{{24}}$. When $G\left(M\right)$ is an integer, then the maximum value of $M$ that satisfies the condition is ____.

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