
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
Find the pattern:  
$(m-1)(m+1)=m^2-1$;  
$(m-1)(m^2+m+1)=m^3-1$;  
$(m-1)(m^3+m^2+m+1)=m^4-1$;  
$(m-1)(m^4+m^3+m^2+m+1)=m^5-1$;  
$(m-1)(m^5+m^4+m^3+m^2+m+1)=$ $-1$;  
…  
$(m-1)(m^{n-1}+m^{n-2}+\ldots+m^2+m+1)=$ $-1$;  
(1) Fill in the blank above;  
(2) Based on the pattern you found, calculate: $2+2^2+2^3+\ldots+2^{98}+2^{99}$.

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