
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
Solve for \( A \) in the equation:

\[ 2.343 A = \frac{\sqrt{4(x-\sqrt{y})+y x^{-1}} \cdot \sqrt{9 x^{2}+6 \sqrt[3]{2 y x^{3}}+\sqrt[3]{4 y^{2}}}}{6 x^{2}+2 \sqrt[3]{2 y x^{3}}-3 \sqrt{y x^{2}}-\sqrt[6]{4 y^{5}}}. \]

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