
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
Konstantin moves a knight on a  $n \times n$ - chess board from the lower left corner to the lower right corner with the minimal number of moves.

Then Isabelle takes the knight and moves it from the lower left corner to the upper right corner with the minimal number of moves.

For which values of  $n$  do they need the same number of moves?

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