
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
At the "Lukomorye" station, tickets are sold for one, five, and twenty trips. All tickets cost an integer number of gold coins. Five single-trip tickets are more expensive than one five-trip ticket, and four five-trip tickets are more expensive than one twenty-trip ticket. It turned out that the cheapest way for 33 warriors to travel was to buy tickets for 35 trips, spending 33 gold coins. How much does a five-trip ticket cost?

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