
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 order to better protect the picturesque Anju Qiongjiang River, the Anju District sewage treatment plant decided to purchase a total of 20 units of type $A$ and $B$ sewage treatment equipment to treat the sewage around the Anju Qiongjiang River. Each unit of type $A$ sewage treatment equipment costs 120,000 yuan, and each unit of type $B$ sewage treatment equipment costs 100,000 yuan. It is known that 1 unit of type $A$ sewage treatment equipment and 2 units of type $B$ sewage treatment equipment can process 640 tons of sewage per week, and 2 units of type $A$ sewage treatment equipment and 3 units of type $B$ sewage treatment equipment can process 1080 tons of sewage per week.  
$(1)$ Find out how many tons of sewage each unit of type $A$ and $B$ sewage treatment equipment can process per week.  
$(2)$ According to the budget, the funds for purchasing equipment at the Anju District sewage treatment plant should not exceed 2.3 million yuan, and the amount of sewage processed per week should not be less than 4500 tons. Please list all purchasing plans and indicate which plan requires the least amount of funds and what is the minimum amount.

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