
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
Esmeralda has created a special knight to play on quadrilateral boards that are identical to chessboards. If a knight is in a square then it can move to another square by moving 1 square in one direction and 3 squares in a perpendicular direction (which is a diagonal of a  $2\times4$  rectangle instead of  $2\times3$  like in chess). In this movement, it doesn't land on the squares between the beginning square and the final square it lands on.

A trip of the length  $n$  of the knight is a sequence of  $n$  squares  $C1, C2, ..., Cn$  which are all distinct such that the knight starts at the  $C1$  square and for each  $i$  from  $1$  to  $n-1$  it can use the movement described before to go from the  $Ci$  square to the  $C(i+1)$ .

Determine the greatest  $N \in \mathbb{N}$  such that there exists a path of the knight with length  $N$  on a  $5\times5$  board.

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