
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
Let  $n$  be a positive integer. A panel of dimenisions  $2n\times2n$  is divided in  $4n^2$  squares with dimensions  $1\times1$ . What is the highest possible number of diagonals that can be drawn in  $1\times1$  squares, such that each two diagonals have no common points. 

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