
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
Professor Guilherme created three strange machines. Machine $A$ transforms a cat into a dog with a probability of $\frac{1}{3}$. Machine $B$ transforms a cat into a dog with a probability of $\frac{2}{5}$. Machine $C$ transforms a cat into a dog with a probability of $\frac{1}{4}$. If the animal is a dog, none of the machines will perform any transformation.

Professor Guilherme put a cat into machine $A$, then put the resulting animal from machine $A$ into machine $B$, and finally put the resulting animal from machine $B$ into machine $C$. What is the probability that a dog came out of machine $C$?



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