
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 $\frac{1}{\sqrt{3} + \sqrt{5} + \sqrt{11}}$ and express your answer in the form \[
\frac{A\sqrt{B} + C\sqrt{D} + E\sqrt{F} + G\sqrt{H}}{I}
\] where $A, B, C, D, E, F, G, H, I$ are integers, everything is in simplest radical form and the fraction is in lowest terms, and $I$ is positive. What is $A+B+C+D+E+F+G+H+I$?

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