
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
Carefully observe the following pattern: $2^2 - 2 = 2(2-1) = 2$; $2^3 - 2^2 = 2^2(2-1) = 2^2$; $2^4 - 2^3 = 2^3(2-1) = 2^3$... (Now you must have noticed a certain pattern, continue with the following questions; the result can be kept in exponential form)  
(1) $2^{100} - 2^{99} =$      
(2) $2^n - 2^{n-1} =$      
(3) Calculate: $2 - 2^2 - 2^3 - 2^4 - … - 2^{2013} + 2^{2014}$ (Don't forget to write the complete calculation process)

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