
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
We need to calculate the expression with three significant digits' accuracy. To simplify the division, find an expression of the form (2) - with coefficients $A, B, C$ such that when multiplying it by (1), we obtain a rational denominator (a formula table can be used).

$$
\begin{gathered}
529 \\
\hline 12 \sqrt[3]{9}+52 \sqrt[3]{3}+49 \\
A \sqrt[3]{9}+B \sqrt[3]{3}+C
\end{gathered}
$$

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