
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
A travel agency rents two types of buses, type \\(A\\) and type \\(B\\), to arrange travel for \\(900\\) passengers. The capacity of type \\(A\\) and type \\(B\\) buses are \\(36\\) and \\(60\\) passengers respectively, and the rental costs are \\(1600\\) yuan per bus for type \\(A\\) and \\(2400\\) yuan per bus for type \\(B\\). The travel agency requires that the total number of buses rented does not exceed \\(21\\) buses, and the number of type \\(B\\) buses should not exceed the number of type \\(A\\) buses by more than \\(7\\). How many buses of each type should be rented to minimize the rental cost, and what is the minimum rental cost?

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