
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
Let the price of a pound of rice be \( x \) coins, the price of a pound of lean sugar be \( y \) coins, and the price of a pound of refined sugar be \( z \) coins. We get the system:

\[
\left\{\begin{array}{l}
4 x + \frac{9}{2} y + 12 z = 6; \\
12 x + 6 y + 6 z = 8
\end{array}\right.
\]

Subtract the first equation from twice the second equation and express \( y \) in terms of \( x \). We get \( y = \frac{4}{3} - \frac{8}{3} x \). Substitute into the second equation and express \( z \) in terms of \( x \): \( z = \frac{2}{3} x \). Find the total cost of the purchase:

\[
4 x + 3 y + 6 z = 4 x + 4 - 8 x + 4 x = 4
\]

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