
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 any three-digit number $n$, if we add the hundreds digit and the tens digit of $n$, and put the resulting digit in the units place of $n$, the four-digit number obtained is called the "lucky number" of $n$. Then the "lucky number" of $571$ is ______. For a lucky number $N=\overline{abcd}$, where the two-digit number formed by the hundreds and tens digits is $\overline{ab}$, and the two-digit number formed by the units and tens digits is $\overline{dc}$, it is defined that ${F(N)=\frac{\overline{ab}-\overline{dc}}{3}}$. If a three-digit number $s=100x+10y+103(x\geq y$ and $0\leq y,x\leq 8)$, its "lucky number" $t$ is divisible by $17$ with a remainder of $5$, and $F\left(t\right)$ is an integer, then the maximum value of $s$ that satisfies the conditions is ______.

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