
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
Let $$\overset{ .}{a_{n}a_{n-1}a_{n-2}\cdots a_{1}a_{0}}|_{m}$$ be defined as $a_{0}+a_{1}\times m+\ldots+a_{n-1}\times m^{n-1}+a_{n}\times m^{n}$, where $n\leq m$, $m$ and $n$ are positive integers, $a_{k}\in\{0,1,2,\ldots,m-1\}$ ($k=0,1,2,\ldots,n$) and $a_{n}\neq 0$;  
(1) Calculate $$\overset{ .}{2016}|_{7}$$\= \_\_\_\_\_\_ ;  
(2) Let the set $A(m,n)=$$\{x|x= \overset{ .}{a_{n}a_{n-1}a_{n-2}\cdots a_{1}a_{0}}|_{m}\}$, then the sum of all elements in $A(m,n)$ is \_\_\_\_\_\_ .

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