
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 two two-digit numbers $p$ and $q$, by placing the tens digit and the units digit of either number between the tens and units digits of the other number and to the right of the units digit, two new four-digit numbers are obtained. Let the quotient of the sum of these two new four-digit numbers divided by $11$ be denoted as $F(p,q)$. If $a=10+m$, $b=10n+5$, where $0\leq m\leq 9$, $1\leq n\leq 9$, $m$ and $n$ are natural numbers. When $150F(a,18)+F(b,26)=32761$, then the value of $m+n$ is ____.

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