
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 ancient Chinese mathematical work "Jiuzhang Suanshu" (The Nine Chapters on the Mathematical Art) contains the following problem: "There is a reed that grows three feet on the first day, and a smilax plant that grows one foot on the first day. Afterwards, the reed grows half of its height from the previous day, while the smilax grows double its previous day's height. How many days will it take for the reed and the smilax to be of equal height?" By using the information provided, we can determine that on the \_\_\_\_\_\_ day, the reed and smilax will be of equal height. (Given that $\log2 = 0.3010$ and $\log3 = 0.4771$, the result should be accurate to one decimal place.)

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