
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
Given two positive numbers $a$ and $b$, a new number $c$ can be generated according to the rule $c=ab+a+b$. By selecting the two larger numbers among $a$, $b$, and $c$ and applying the aforementioned rule, a new number is generated. This process is repeated, and each generation of a new number is considered one operation. If $p > q > 0$, and after 6 operations, the generated number is $(q+1)^m(p+1)^n-1$ (where $m$ and $n$ are positive integers), then the value of $m+n$ is $\_\_\_\_\_\_$.

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