
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
According to relevant data statistics, through environmental remediation, the relationship between the polluted area $S$ (in km$^2$) of a certain lake and time $t$ (in years) can be approximately regarded as an exponential function. It is known that the polluted area has decreased from 0.16 km$^2$ to 0.04 km$^2$ over the past two years. How many more years will it take for the polluted area to decrease to 0.01 km$^2$?

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