
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 
\[\begin{aligned} 
p &= 2\sqrt{2} + 3\sqrt{3} + 2\sqrt{6}, \\
q &= -2\sqrt{2} + 3\sqrt{3} + 2\sqrt{6}, \\
r &= 2\sqrt{2} - 3\sqrt{3} + 2\sqrt{6}, \\
s &= -2\sqrt{2} - 3\sqrt{3} + 2\sqrt{6}. 
\end{aligned}\]
Evaluate \(\left(\frac{1}{p} + \frac{1}{q} + \frac{1}{r} + \frac{1}{s}\right)^2.\)

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