
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
There is a piece of paper. The first time it is divided into 4 pieces, the second time one of those pieces is divided into 4 pieces, and so on, with each subsequent division dividing one of the pieces obtained from the previous division.  
(1) After 5 divisions, there are a total of ___ pieces of paper; after $n$ divisions, there are a total of ___ pieces of paper (expressed as an algebraic expression involving $n$).  
(2) Is it possible to have a total of 2011 pieces of paper after a certain number of divisions? Please explain through calculation.

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