You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
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Water is the source of life and one of the indispensable important material resources for human survival and development. In order to better manage water quality and protect the environment, the Municipal Sewage Treatment Office plans to purchase 10 sewage treatment equipment in advance. There are two models, $A$ and $B$, with their prices and sewage treatment capacities as shown in the table below:<br/>

|          | $A$ model | $B$ model |
|----------|-----------|-----------|
| Price (million yuan) | $12$ | $10$ |
| Sewage treatment capacity (tons/month) | $240$ | $200$ |

$(1)$ In order to save expenses, the Municipal Sewage Treatment Office plans to purchase sewage treatment equipment with a budget not exceeding $105$ million yuan. How many purchasing plans do you think are possible?<br/>
$(2)$ Under the condition in $(1)$, if the monthly sewage treatment volume must not be less than $2040$ tons, to save money, please help the Municipal Sewage Treatment Office choose the most cost-effective plan.
user
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rule
Water is the source of life and one of the indispensable important material resources for human survival and development. In order to better manage water quality and protect the environment, the Municipal Sewage Treatment Office plans to purchase 10 sewage treatment equipment in advance. There are two models, $A$ and $B$, with their prices and sewage treatment capacities as shown in the table below:<br/>

|          | $A$ model | $B$ model |
|----------|-----------|-----------|
| Price (million yuan) | $12$ | $10$ |
| Sewage treatment capacity (tons/month) | $240$ | $200$ |

$(1)$ In order to save expenses, the Municipal Sewage Treatment Office plans to purchase sewage treatment equipment with a budget not exceeding $105$ million yuan. How many purchasing plans do you think are possible?<br/>
$(2)$ Under the condition in $(1)$, if the monthly sewage treatment volume must not be less than $2040$ tons, to save money, please help the Municipal Sewage Treatment Office choose the most cost-effective plan.
train