
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
Before the math competition, Dmytro overheard Olena and Mykola talking about their birthdays.**О**: "The day and month of my birthday are half as large as the day and month of Mykola's birthday."**М**: "Also, the day of Olena's birth and the month of my birth are consecutive positive integers."**О**: "And the sum of all these four numbers is a multiple of  $17$ ."

Can Dmitro determine the day and month of Olena's birth?

*Proposed by Olena Artemchuk and Mykola Moroz*

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