
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
In the following product, convert each of the two factors into fractions and then express the numerator as the product of 4 numbers. How can we write the numerator if, instead of $a+b+c+d$, we use $2s$?

$$
\left(1+\frac{a^{2}+b^{2}-c^{2}-d^{2}}{2(a b+c d)}\right) \cdot\left(1-\frac{a^{2}+b^{2}-c^{2}-d^{2}}{2(a b+c d)}\right)
$$

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