
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
In Miroslav's kingdom, cobbler Matěj would visit not only to sing but also to eat and drink well. For one gold coin, he would receive a whole goose and a jug of wine. However, the prices increased by $20\%$ and for a gold coin, he would now receive only half a jug of wine and a whole goose. It is rumored that after the full moon, prices will rise by another $20\%$. Will Matěj still get at least one whole goose for his gold coin?

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