
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 \(\frac{1}{\sqrt{5} + \sqrt{6} + \sqrt{8}}\) and express your answer in the form
\[
\frac{A\sqrt{p} + B\sqrt{q} + C\sqrt{r} + D\sqrt{S}}{F},
\]
where each term is in simplest radical form and \(F\) is positive. Calculate \(A + B + C + D + S + F\).

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