
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
"The green hills and clear waters are as valuable as mountains of gold and silver." In order to beautify the ecological environment and create a comfortable living environment for residents, the Chongqing Municipal Government plans to transform a section of the riverside road into a riverside promenade. In the first phase of the project, a total of 7000 tons of slag soil need to be transported away. It is planned that two construction teams, Team A and Team B, will be responsible for transporting the slag soil. It is known that in the original plan, Team A was supposed to transport on average $\frac{2}{3}$ more slag soil per day than Team B. In this way, the time it takes for Team A to transport 4000 tons of slag soil is two days less than the time it takes for Team B to transport the remaining slag soil.  
$(1)$ Find out how many tons of slag soil Team A was supposed to transport on average per day in the original plan.  
$(2)$ During the actual construction, Team A increased their average daily transport by $m$ tons compared to the original plan, while Team B increased their average daily transport by $\frac{m}{300}$. After working together for 7 days, Team A had to attend to other tasks; the remaining slag soil was then completed by Team B working alone for 2 more days. If the transportation cost per ton of slag soil is $50 yuan, calculate the transportation cost for Team B.

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