
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
Given one gallon of paint is used, one fourth is used on the first day, one half of the remaining paint is used on the second day, and one third of what is left after the second day is used on the third day, determine the fraction of the original amount of paint that is left after the third day.

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