
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
The sound intensity level $Y$ (unit: decibels) is given by the formula $Y=10\lg \left( \frac{I}{10^{-12}} \right)$, where $I$ is the sound intensity (unit: $W/m^{2}$).

$(1)$ The sound intensity of ordinary conversation is about $10^{-6}W/m^{2}$. Calculate its sound intensity level;

$(2)$ The lowest sound intensity level that ordinary people can hear is $0$ decibels. What is the lowest sound intensity they can hear?

$(3)$ A more ideal sleeping environment requires the sound intensity level $Y \leqslant 50$ decibels. Knowing that the sound intensity of two students talking in the dormitory after lights out is $5×10^{-7}W/m^{2}$, do these students disturb the rest of the others?

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