
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
A food factory processes mushrooms, with a cost of 20 yuan per kilogram of mushrooms, and a processing fee of t yuan per kilogram (t is a constant, and $2 \leq t \leq 5$). Assume the factory price per kilogram of mushrooms is x yuan ($25 \leq x \leq 40$). According to market research, the sales volume q is inversely proportional to $e^x$, and when the factory price per kilogram of mushrooms is 30 yuan, the daily sales volume is 100 kilograms.  
(1) Find the relationship between the factory's daily profit y yuan and the factory price per kilogram of mushrooms x yuan;  
(2) If $t = 5$, what is the factory price per kilogram of mushrooms x for the factory's profit y to be maximized, and find the maximum value.

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