
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 $(x_1,y_1),$ $(x_2,y_2),$ $\dots,$ $(x_n,y_n)$ be the solutions to the system
\begin{align*}
|x - 5| &= |y - 7|, \\
|x - 7| &= 3|y - 5|.
\end{align*}
Find $x_1 + y_1 + x_2 + y_2 + \dots + x_n + y_n.$

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