
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
Jorge, who lives in Recife, corresponds with his English friend Ralph, who lives in England. They understand each other very well in both languages, but they have a problem with dates. In Brazil, the date 08/10 means October 8th, while in England, it means August 10th. Because of this, they agreed not to write to each other on days when the date is ambiguous. They prefer dates like 25/03, which can only mean March 25th.

(a) On which of the following dates can Jorge and Ralph not write to each other?
(i) December 3rd
(ii) August 18th
(iii) May 5th

(b) When do the longest periods occur in which the two friends cannot write to each other?

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