
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
Rózsa, Ibolya, and Viola have decided to solve all the problems in their problem collection. Rózsa solves \(a\), Ibolya \(b\), and Viola \(c\) problems daily. (Only one of them works on a problem.) If Rózsa solved 11 times, Ibolya 7 times, and Viola 9 times more problems daily, they would finish in 5 days; whereas if Rózsa solved 4 times, Ibolya 2 times, and Viola 3 times more problems daily, they would finish in 16 days. How many days will it take for them to complete the solutions?

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