
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
Let 
\[
\begin{aligned} 
a &= \sqrt{2} + \sqrt{3} + \sqrt{5}, \\ 
b &= -\sqrt{2} + \sqrt{3} + \sqrt{5}, \\ 
c &= \sqrt{2} - \sqrt{3} + \sqrt{5}, \\ 
d &= -\sqrt{2} - \sqrt{3} + \sqrt{5}. 
\end{aligned}
\]
Evaluate $\left(\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d}\right)^2$.

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