
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
Two painters are painting 100 sections of a fence around a villa. They alternate working days, with each painter painting one section of the fence each working day. The fence sections can be painted either red or green. The first painter is colorblind and cannot distinguish between the colors, but he can remember the sections and colors he has painted and can also see which sections the second painter has painted, although he does not know their colors. The first painter wants to maximize the number of red-green alternations on the fence. What is the maximum number of red-green alternations he can achieve, regardless of how the second painter works?

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