
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 \[\begin{aligned} 
a &= \sqrt{2}^2+\sqrt{3}+\sqrt{5}, \\
b &= -\sqrt{2}^2+\sqrt{3}+\sqrt{5}, \\
c &= \sqrt{2}^2-\sqrt{3}+\sqrt{5}, \\
d &= -\sqrt{2}^2-\sqrt{3}+\sqrt{5}.
\end{aligned}\]
Evaluate $\left(\frac1a + \frac1b + \frac1c + \frac1d\right)^2$.

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