
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 a certain shopping mall in Taiyuan City, a certain brand of clothing with a cost price of $100 is found to sell 100 pieces per day when the selling price is set at $200 during the sales period. As the National Day and Mid-Autumn Festival of 2023 approaches, the store decides to launch a major promotion. After research, it is found that when the selling price decreases by $1, the daily sales volume increases by 4 pieces. Let $x$ represent the price reduction per item of the brand clothing.

$(1)$ Find the function relationship of the daily sales volume $y$ (in pieces) with respect to $x$ (in dollars).

$(2)$ Assuming the selling price is not less than $150, calculate the selling price at which the store makes a daily profit of $13600.

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