
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
Petya wrote a 100-digit number \( X \) that does not contain any zeros. The 50-digit number formed by the first fifty digits of \( X \), Petya called the head of \( X \). It turned out that the number \( X \) is divisible by its head without remainder. How many zeros are there in the quotient?

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