
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 \[\begin{aligned} 
p &= \sqrt{5}+\sqrt{7}+\sqrt{35}, \\ 
q &= -\sqrt{5}+\sqrt{7}+\sqrt{35}, \\ 
r &= \sqrt{5}-\sqrt{7}+\sqrt{35}, \\ 
s &= -\sqrt{5}-\sqrt{7}+\sqrt{35}. 
\end{aligned}\]
Evaluate \(\left(\frac1p + \frac1q + \frac1r + \frac1s\right)^2.\)

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