
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 factory plans to produce two types of student desks and chairs, type A and type B, for a disaster-stricken school, aiming to accommodate 1250 students with a total of 500 sets. Type A (one desk and two chairs) requires 0.5m³ of wood, while type B (one desk and three chairs) requires 0.7m³ of wood. The factory currently has a wood inventory of 302m³.

1. How many production plans are possible?
2. All produced desks and chairs will be shipped to the disaster area. Given that the production cost for each set of type A is 100 yuan with a shipping fee of 2 yuan, and the production cost for each set of type B is 120 yuan with a shipping fee of 4 yuan, derive the relationship between the total cost y (in yuan) and the number of type A sets produced x (in sets). Determine the production plan with the least total cost and the corresponding minimum total cost. (Total cost = production cost + shipping fee)

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