
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
\begin{align*}
|x - 4| &= |y - 10|, \\
|x - 10| &= 3|y - 4|.
\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