
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 teacher wrote an arithmetic problem on the board: the product of two mixed fractions equals 43. Then he replaced the denominator of the first fraction with $X$ and the whole part of the second fraction with $Y$. The resulting expression is:

\[ 5 \frac{1}{X} \cdot Y \frac{1}{2}=43 \]

Restore the original problem.

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