
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
\[
\begin{aligned}
a &= 2\sqrt{5}+\sqrt{7}+\sqrt{35}, \\
b &= -2\sqrt{5}+\sqrt{7}+\sqrt{35}, \\
c &= 2\sqrt{5}-\sqrt{7}+\sqrt{35}, \\
d &= -2\sqrt{5}-\sqrt{7}+\sqrt{35}.
\end{aligned}
\]
Evaluate $\left(\frac1a + \frac1b + \frac1c + \frac1d\right)^2.$

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