
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 8-by-8 square is divided into 64 unit squares in the usual way.  Each unit square is colored black or white.  The number of black unit squares is even.  We can take two adjacent unit squares (forming a 1-by-2 or 2-by-1 rectangle), and flip their colors: black becomes white and white becomes black.  We call this operation a *step*.  If  $C$  is the original coloring, let  $S(C)$  be the least number of steps required to make all the unit squares black.  Find with proof the greatest possible value of  $S(C)$ .

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