
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 company has 600,000 yuan in funds and plans to invest in projects A and B. The investment in project A must not be less than $\frac{2}{3}$ of the investment in project B, and the investment in each project cannot be lower than 50,000 yuan. For every 10,000 yuan invested in project A, a profit of 4,000 yuan can be obtained, while for every 10,000 yuan invested in project B, a profit of 6,000 yuan can be obtained. How should the company plan its investment to maximize the combined profit from the two projects, and what is the maximum profit?

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