
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 a maximum impurity content of $0.1%$ according to market requirements. Initially, the produced solution contains $2%$ impurities, and each filtration process can reduce the impurity content by $\frac{1}{2}$. To meet the market requirements, the solution should be filtered at least $\_\_\_\_\_\_\_\_$ times.

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