
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
The musical theater announced a competition for admission to the orchestra. Initially, it was assumed that the number of places for violinists, cellists, and trumpeters would be distributed in the ratio $1.6: 1: 0.4$. However, it was then decided to increase the admission, and as a result, the number of violinists admitted was $25\%$ more, and the number of cellists was $20\%$ less than originally planned. How many musicians of each genre were admitted to the orchestra if a total of 32 people were admitted?

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