
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
A rectangle \( R \) is divided into 2016 smaller rectangles, with each smaller rectangle's sides parallel to the sides of rectangle \( R \). The vertices of the smaller rectangles are called "nodes". A segment on the side of a smaller rectangle, if both its endpoints are nodes and its interior contains no other nodes, is called a "basic segment". Consider all possible ways of dividing the rectangle \( R \). Find the maximum and minimum number of basic segments.

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