
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
On the fields of a chesstable of dimensions  $ n\times n$ , where  $ n\geq 4$  is a natural number, are being put coins. We shall consider a *diagonal* of table each diagonal formed by at least  $ 2$  fields. What is the minimum number of coins put on the table, s.t. on each column, row and diagonal there is at least one coin? Explain your answer.

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