
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
Alina and Masha wanted to create an interesting version of the school tour of the Olympiad. Masha proposed several problems and rejected every second problem of Alina (exactly half). Alina also proposed several problems and only accepted every third problem of Masha (exactly one-third). In the end, there were 10 problems, and initially, 27 problems were proposed. How many more problems did Masha propose compared to Alina?

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