
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 thousand digit and the tens digit of a four-digit positive integer are the same, and the hundreds digit and the units digit are the same, we call this four-digit number a "blended number." By exchanging the digits in the thousand and hundred places of the "blended number" $t$, and also exchanging the digits in the tens and units places, we obtain a new number $t'$. Let $F(t)=\frac{2(t+t')}{1111}$. If $m$ is the largest "blended number," then $F(m)=\_\_\_\_\_\_$. Given two "blended numbers" $p$ and $q$, where $p=\overline{abab}$ and $q=\overline{cdcd}$ (where $1\leqslant a \lt b\leqslant 9$, $1\leqslant c\leqslant 9$, $1\leqslant d\leqslant 9$, $c\neq d$, and $a$, $b$, $c$, $d$ are all integers). If $F(p)$ is divisible by $17$, and $F(p)+2F(q)-(4a+3b+2d+c)=0$, then the value of $F(p-q)$ is ______.

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