
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
In Kocourkov, there are coins with exactly two different denominations, expressed as positive integers in Kocourkov crowns. Using a sufficient number of such coins, it is possible to pay any integer amount greater than 53 Kocourkov crowns exactly, without requiring change. However, the amount of 53 Kocourkov crowns cannot be paid exactly without returning any change.

Determine which denominations the Kocourkov coins could have. Provide at least two such solutions.

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