
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
In Xiaocaoba Town, Yiliang County, Zhaotong City, which is the original production area of Urtica fissa, Urtica fissa has been on the market recently. A company has launched a special gift box of Urtica fissa with a cost of $70$ yuan. When the selling price per box is $120$ yuan, the company can sell $300$ boxes per week. In order to increase market share, while ensuring profitability, the company takes price reduction measures. According to market research, for every $1$ yuan reduction per box, the weekly sales volume can increase by $10$ boxes. <br/>$(1)$ Write down the function relationship between the company's weekly profit $W$ yuan and the price reduction $x$ yuan; <br/>$(2)$ When the price is reduced by how many yuan, the company's weekly profit is maximized, and what is the maximum amount in yuan? <br/>$(3)$ If the company's weekly profit needs to reach $15960$ yuan and maximize benefits to the public, what should be the price?

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