
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 processing factory is involved in the deep processing of mushrooms. The cost per kilogram of mushrooms is $20, and the processing fee per kilogram of mushrooms is $t$ ($t$ is a constant, and $2 \leqslant t \leqslant 5$). Let the ex-factory price per kilogram of mushrooms be $x$ ($25 \leqslant x \leqslant 40$). According to a market survey, the sales volume $q$ is inversely proportional to $e^{x}$. When the ex-factory price per kilogram of mushrooms is $30, the daily sales volume is 100 kilograms.

(1) Find the function relationship between the daily profit $y$ (in dollars) of the factory and the ex-factory price $x$ (in dollars) per kilogram of mushrooms;

(2) If $t=5$, what is the ex-factory price $x$ per kilogram of mushrooms that maximizes the factory's daily profit? Calculate the maximum value.

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