
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  $n > 4$  be an integer. A square is divided into  $n^2$  smaller identical squares, in some of which were **1’s** and in the other – **0's**. It is not allowed in one row or column to have the following arrangements of adjacent digits in this order:  $101$ ,  $111$  or  $1001$ . What is the biggest number of **1’s** in the table? (The answer depends on  $n$ .) 

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