
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
Factorize the following expression:

$$
\begin{aligned}
& (a p+b q+c r+d s)^{2}+(a q-b p+c s-d r)^{2}+ \\
& +(a r-b s-c p+d q)^{2}+(a s+b r-c q-d p)^{2}
\end{aligned}
$$

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