
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 shelf life $y$ (in hours) of a certain food product is related to its storage temperature $x$ (in degrees Celsius) by the function $y = e^{kx+b}$ (where $e=2.718\ldots$ is the base of the natural logarithm, and $k$, $b$ are constants). It is known that the shelf life of the product at $0°C$ is $160$ hours, and at $20°C$ is $40$ hours.
(1) Find the shelf life of the product at $30°C$;
(2) If the shelf life of the product must be at least $80$ hours, what condition must the storage temperature satisfy?

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