
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
In each square of a  $5 \times 5$  board one of the numbers  $2, 3, 4$  or  $5$  is written so that the the sum of all the numbers in each row, in each column and on each diagonal is always even. How many ways can we fill the board?

Clarification. A  $5\times 5$  board has exactly  $18$  diagonals of different sizes. In particular, the corners are size  $ 1$  diagonals.

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