
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 with an initial impurity content of $10%$. Each filtration process reduces the impurity content by $\frac{1}{3}$. To meet the market requirement of an impurity content not exceeding $0.5%$, the solution must be filtered at least $\_\_\_\_\_\_$ times. Given that $\lg 2=0.3010$ and $\lg 3=0.4771$.

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