
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 2 gallons of paint are required for the room's complete coverage, determine the fraction of the original amount of paint available to use on the third day, given that one quarter of the paint is used on the first day and one third of the remaining paint is used on the second day.

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