
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
An ancient Chinese mathematical text, "The Nine Chapters on the Mathematical Art," presents the following problem: "Suppose there is a plant called Pu (a type of aquatic plant) that grows three feet in one day, and there is another plant called Guan (also known as water scallion or mat grass), which grows one foot in one day. The growth of Pu halves each day, while the growth of Guan doubles each day. After how many days will their lengths be equal?" The growth over one day for Pu is 3 feet and for Guan is 1 foot. If the growth rate of Pu is halved daily, and the growth of Guan doubles daily, they will be of equal length after approximately ____ days. (Round the result to one decimal place; reference data: lg2 ≈ 0.30, lg3 ≈ 0.48)

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