
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 both understand each other well in both languages but have a problem with dates: the date $08 / 10$ in Brazil means October 8th, and in England, it means August 10th. Because of this, they agreed not to write to each other on dates that could be 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 is the longest period during which the two friends cannot write to each other?

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