
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 positive integer $M=\overline{abcd}$, if $a-b=c-d$, then $M$ is called a "friendly number". Let $s$ be the three-digit number obtained by removing the units digit of the "friendly number" $M$, and let $t$ be the three-digit number obtained by removing the thousands digit. Define $F(M)=s-t-10b$. Find $F(\overline{3153})=\_\_\_\_\_\_$. If a four-digit positive integer $N=1000x+100y+30m+n+1001$ (where $0\leqslant y \lt x\leqslant 8$, $0\leqslant m\leqslant 3$, $0\leqslant n\leqslant 8$, $x$, $y$, $m$, $n$ are integers) is a "friendly number" and $F(N)$ leaves a remainder of $1$ when divided by $5$, then find the maximum value of such $N$.

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