
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 store purchases a certain product at a cost of 30 yuan per item. During a trial sale, it was discovered that the daily sales volume $m$ (in pieces) and the selling price $x$ (in yuan per piece) satisfy a linear function $m = 162 - 3x$, where $30 \leq x \leq 54$.

(1) Establish the function that describes the relationship between the daily profit $y$ from selling this product and the selling price $x$ per piece.

(2) If the store wants to maximize its daily profit from selling this product, what should the selling price per item be? What is the maximum daily profit?

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