
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
Solve the following two equations:

$$
\begin{aligned}
& \sqrt{(x-1)(x-2)}+\sqrt{(x-3)(x-4)}=\sqrt{2} \\
& \sqrt{(x-p-q)(x-p+q)}+\sqrt{(x-r-q)+(x-r+q)}=\sqrt{(p-r)(p-r)(p-r+2q)}
\end{aligned}
$$


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