
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 the relationship between the residual amount $y$ of a certain brand of plastic bag after natural degradation and time $t$ in years given by $y=y_{0}e^{kt}$, where $y_{0}$ is the initial amount, and $k$ is the photodegradation coefficient, determine the time $t$ for the residual amount of this brand of plastic bag to be $10\%$ of the initial amount.

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