
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
Given the monthly sales volume $x$ in ten thousand units of the product satisfies the functional relationship with the cost of investing in physical store experience installation $t$ in ten thousand yuan given by $x=3-\frac{2}{{t+1}}$, the fixed monthly expenses for the online store are 30,000 yuan, and the purchase price of the product per ten thousand units is 320,000 yuan. 

The selling price of each product is set as the sum of "150% of the purchase price" and "half of the average cost of physical store experience installation per product." Determine the maximum monthly profit of the company.

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