
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
Sasha and Serg plays next game with  $100$ -angled regular polygon . In the beggining Sasha set natural numbers in every angle. Then they make turn by turn, first turn is made by Serg. Serg turn is to take two opposite angles and add  $1$  to its numbers. Sasha turn is to take two neigbour angles and add  $1$  to its numbers. Serg want to maximize amount of odd numbers. What maximal number of odd numbers can  he get no matter how Sasha plays?

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