
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
Online stores and physical stores each have their advantages and disadvantages, and the combination of the two will become a major development direction in business for a period of time in the future. A brand of dash cam mounts sales company started a sales model combining online sales with physical store experience and installation from January 2017. According to several months of operation, it was found that the monthly sales volume \(x\) (in ten thousand units) and the cost \(t\) (in ten thousand yuan) invested in physical store experience and installation satisfy the function relationship \(x=3- \dfrac{2}{t+1}\). Given that the store's fixed monthly expenses are 3 ten thousand yuan, and the purchase price for every ten thousand units of the product is 32 ten thousand yuan, if the selling price of each product is set as "150% of the purchase price" plus "half of the average cost per unit for physical store experience and installation", then the maximum monthly profit of the company is ______ ten thousand yuan.

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