
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  $A$  be a  $n\times n$  matrix such that  $A_{ij} = i+j$ . Find the rank of  $A$ .

<details><summary>Remark</summary>Not asked in the contest:  $A$  is diagonalisable since real symetric matrix it is not difficult to find its eigenvalues.</details>

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