
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
An  $n \times n$  complex matrix  $A$  is called \emph{t-normal} if $AA^t = A^t A$  where  $A^t$  is the transpose of  $A$ .  For each  $n$ ,
determine the maximum dimension of a linear space of complex  $n
\times n$  matrices consisting of t-normal matrices.

Proposed by Shachar Carmeli, Weizmann Institute of Science


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