
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 city road renovation project, if Team A works alone, it would take 30 days to complete. If Team B works alone, it would take 60 days to complete. The daily construction cost for Team A is 25,000 yuan, and for Team B, it is 10,000 yuan. Please answer the following questions:  
(1) How many days would it take for Teams A and B to complete the project if they work together?  
(2) After working together for 10 days, Team A has to leave for another task, and Team B continues the work alone. How many days in total are needed to complete the project?  
(3) To ensure the total construction cost does not exceed 650,000 yuan, what is the maximum number of days Teams A and B can work together?  
(4) If the project must be completed within 24 days (including the 24th day), how should the work be arranged between the two teams to minimize the construction cost? Please describe your arrangement and calculate the required construction cost.

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