
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
Explore and Think: When calculating the sum of $m+m^2+m^3+…+m^n$, we can use the following approach:  
Let $A=m+m^2+m^3+…+m^n$, then $mA=m^2+m^3+…+m^{n+1}$;  
(1) Try to use the above approach to find the sum of $m+m^2+m^3+…+m^n$;  
(2) Please use the result of (1) to find the sum of $m+2m^2+3m^3+…+nm^n$.

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