
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
Eva and Marek were playing badminton while Viktor tallied the rallies. After every 10 rallies, Viktor drew an X. Later, he replaced every 10 Xs with an O and erased the corresponding 10 Xs. When Eva and Marek finished the game, Viktor had drawn the following:

## OOOXXXXXXX

Determine the minimum and maximum number of rallies Eva and Marek could have played.

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