
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
Mrs. Široká was expecting guests in the evening. First, she prepared 25 open-faced sandwiches. She then calculated that if each guest took two sandwiches, three of them would not have enough. She then thought that if she made 10 more sandwiches, each guest could take three, but four of them would not have enough. This still seemed insufficient to her. Finally, she prepared a total of 52 sandwiches. Each guest could then take four sandwiches, but not all of them could take five. How many guests was Mrs. Široká expecting? She herself is on a diet and never eats in the evening.

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