
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
Edward's formula for the stock market predicts correctly that the price of HMMT is directly proportional to a secret quantity  $ x$  and inversely proportional to  $ y$ , the number of hours he slept the night before. If the price of HMMT is  $ \$ 12 $ when $  x\equal{}8 $ and $  y\equal{}4 $, how many dollars does it cost when $  x\equal{}4 $ and $  y\equal{}8$?

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