
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 expanded according to the rule $c=ab+a+b$. Among the numbers $a$, $b$, and $c$, take the two larger numbers and expand them according to the above rule to get a new number. This process is repeated, and each expansion to get a new number is called an operation.  
(1) If $a=1$ and $b=3$, perform the operation three times according to the above rule, the expanded number obtained is.  
(2) If $p>q>0$, after 6 operations, the expanded number obtained is $(q+1)^m(p+1)^n-1$ ($m$, $n$ are positive integers), then the values of $m$ and $n$ are.

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