
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
Vegetables are transported from two vegetable villages, $A$ and $B$, to two destinations, $X$ and $Y$. Village $A$ and village $B$ have 80 tons and 60 tons of vegetables, respectively. Destination $X$ requires 65 tons of vegetables, and destination $Y$ requires 75 tons. The transportation cost from village $A$ to destination $X$ is $50$ yuan per ton, and to destination $Y$ is $30$ yuan per ton. The transportation cost from village $B$ to destination $X$ is $60$ yuan per ton, and to destination $Y$ is $45$ yuan per ton. How should the vegetables be transported to minimize the total transportation cost? What is the minimum cost?

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