
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
Rationalize the denominator of \(\frac{5}{4\sqrt{7} - 3\sqrt{2}}\) and write your answer in the form \(\displaystyle \frac{A\sqrt{B} + C\sqrt{D}}{E}\), where \(B < D\), the fraction is in lowest terms, and all radicals are in simplest radical form. What is \(A+B+C+D+E\)?

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