
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 jeweler can get an alloy that is  $40\%$  gold for  $200$  dollars per ounce, an alloy that is  $60\%$  gold for  $300$  dollar per ounce, and an alloy that is  $90\%$  gold for  $400$  dollars per ounce. The jeweler will purchase some of these gold alloy products, melt them down, and combine them to get an alloy that is  $50\%$  gold. Find the minimum number of dollars the jeweler will need to spend for each ounce of the alloy she makes.

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