
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
Given that the function relationship between the residual quantity of pollutants $P$ (unit: milligrams per liter) during the filtering process and the filtering time $t$ (unit: hours) is $P=P_{0}\cdot e^{-kt}$, where $k$ is a constant, $k \gt 0$, and $P_{0}$ is the original quantity of pollutants, calculate the residual amount of pollutants in the waste gas as a percentage of the original pollutants after filtering for a total of $6$ hours, given that they are exactly filtered out by $90\%$ in the first $4$ hours.

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