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

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