
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 1928, there were four dates with a remarkable property: when recorded in the usual manner, the product of the day and the month gives the year in the 20th century. These dates are 28/1/28, 14/2/28, 7/4/28, and 4/7/28.

How many times in the 20th century (from 1901 to 2000 inclusive) does such a property occur? Can you find the year of our century in which the number of such dates is maximal? There is only one such year.

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