
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  $4$  x  $4$  square board is called  $brasuca$  if it follows all the conditions:

     • each box contains one of the numbers  $0, 1, 2, 3, 4$  or  $5$ ;
     • the sum of the numbers in each line is  $5$ ;
     • the sum of the numbers in each column is  $5$ ;
     • the sum of the numbers on each diagonal of four squares is  $5$ ;
     • the number written in the upper left box of the board is less than or equal to the other numbers
the board;
     • when dividing the board into four  $2$  ×  $2$  squares, in each of them the sum of the four
numbers is  $5$ .

How many  $"brasucas"$  boards are there?

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