
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 National Development and Reform Commission, the Ministry of Industry and Information Technology, and the Ministry of Finance announced the "Energy-saving Product Benefit People Project". The public transportation company actively responded by replacing old buses with energy-saving and environmentally friendly buses. They plan to purchase 10 environmentally friendly buses of type $A$ and type $B$, with the price and annual passenger capacity of each as shown in the table below:

|          | Type $A$ | Type $B$ |
|----------|----------|----------|
| Price (in million RMB per bus) | $x$ | $y$ |
| Annual Passenger Capacity (in 10,000 person-times) | $60$ | $100$ |

If they purchase 1 bus of type $A$ and 2 buses of type $B$, the total cost is 400 million RMB. If they purchase 2 buses of type $A$ and 1 bus of type $B$, the total cost is 350 million RMB.

(1) Find the values of $x$ and $y$.

(2) If the company's total cost of purchasing type $A$ and type $B$ buses does not exceed 1200 million RMB, and it ensures that the total annual passenger capacity of the 10 buses on the route is not less than 680, what are the possible purchasing plans?

(3) Under the conditions of (2), which plan minimizes the total cost of purchasing buses? What is the minimum cost in million RMB?

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