
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 the post-disaster reconstruction of the Wenchuan earthquake in Sichuan, a company plans to build a Hope School for the disaster area. After investigating, the company learned that two construction teams, Team A and Team B, have the ability to contract the construction of the school. Team A can complete the construction of the school alone in $1.5$ times the time it takes for Team B. If Team A and Team B work together, they can complete the construction in $72$ days.  
$(1)$ How many days does each team need to complete the construction of the school individually?  
$(2)$ During the construction process, the company sends a technician to the site to supervise the construction quality throughout, requiring a subsidy of $100$ yuan per day. If the average daily cost for Team A to work alone is $0.8$ million yuan, and the company chooses Team B, requiring the total construction cost not to exceed that of Team A, what is the maximum average daily cost for Team B to work alone?

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