
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
A circle contains 100 nonzero numbers. Between each pair of adjacent numbers, their product is written, and the original numbers are erased. The number of positive numbers remains unchanged. What is the minimum number of positive numbers that could have been written initially?

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