
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
Eight people are standing in line at a ticket counter. Four of them each have a 100 Ft bill, and the other four each have a 200 Ft bill, arranged in a random order. The price of a ticket is 100 Ft, and the cash register is initially empty. Everyone wants to buy one ticket. What fraction of the possible orders allows the cashier to issue the tickets without any problems?

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