
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
A chemical plant produces a solution that, according to market requirements, should not contain more than 0.5% impurities. Initially, the impurity content is 10%, and with each filtration, the impurity content is reduced by one-third. Determine the minimum number of filtrations required to meet the market standard, where lg2=0.3010 and lg3=0.4771.

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