
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
Consider a chess board, with the numbers  $1$  through  $64$  placed in the squares as in the diagram below.

\[\begin{tabular}{| c | c | c | c | c | c | c | c |}
\hline
1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 
\hline
9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 
\hline
17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 
\hline
25 & 26 & 27 & 28 & 29 & 30 & 31 & 32 
\hline
33 & 34 & 35 & 36 & 37 & 38 & 39 & 40 
\hline
41 & 42 & 43 & 44 & 45 & 46 & 47 & 48 
\hline
49 & 50 & 51 & 52 & 53 & 54 & 55 & 56 
\hline
57 & 58 & 59 & 60 & 61 & 62 & 63 & 64 
\hline
\end{tabular}\]

Assume we have an infinite supply of knights. We place knights in the chess board squares such that no two knights attack one another and compute the sum of the numbers of the cells on which the knights are placed. What is the maximum sum that we can attain?

Note. For any  $2\times3$  or  $3\times2$  rectangle that has the knight in its corner square, the knight can attack the square in the opposite corner.

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