
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 light intensity at a depth of $5$ meters is $40\%$ of the light intensity at the sea surface, where the light intensity in the sea water decreases with the depth according to the equation $I_{D}=I_{0}e^{-KD}$, find the approximate value of the extinction coefficient $K$.

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