
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 a four-digit natural number $\overline{abcd}$ has digits that are all different and not equal to $0$, and satisfies $\overline{ab}-\overline{bc}=\overline{cd}$, then this four-digit number is called a "decreasing number". For example, the four-digit number $4129$, since $41-12=29$, is a "decreasing number"; another example is the four-digit number $5324$, since $53-32=21\neq 24$, is not a "decreasing number". If a "decreasing number" is $\overline{a312}$, then this number is ______; if the sum of the three-digit number $\overline{abc}$ formed by the first three digits and the three-digit number $\overline{bcd}$ formed by the last three digits of a "decreasing number" is divisible by $9$, then the maximum value of the number that satisfies the condition is ______.

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