
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
For all positive numbers $a$, $b$, $c$, and $d$, evaluate the expression:
\[
(a+b+c+d)^{-1}(a^{-1}+b^{-1}+c^{-1}+d^{-1})(ab+bc+cd+da+ac+bd)^{-1}[(ab)^{-1}+(bc)^{-1}+(cd)^{-1}+(da)^{-1}+(ac)^{-1}+(bd)^{-1}]
\]
A) $\frac{1}{ab+bc+cd+da+ac+bd}$
B) $\frac{1}{a+b+c+d}$
C) $abcd$
D) $\frac{1}{abcd}$
E) $\frac{1}{(abcd)^2}$

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