
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 \[\begin{aligned} 
a &= \sqrt{3}+\sqrt{5}+\sqrt{15}, \\ 
b &= -\sqrt{3}+\sqrt{5}+\sqrt{15}, \\ 
c &= \sqrt{3}-\sqrt{5}+\sqrt{15}, \\ 
d &= -\sqrt{3}-\sqrt{5}+\sqrt{15}. 
\end{aligned}\]
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}
user