
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

The real numbers \(x\) and \(y\) satisfy the equations:

\[ xy - x = 180 \]

\[ y + xy = 208 \]

Let the two solutions be \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\).
What is the value of \(x_{1} + 10 y_{1} + x_{2} + 10 y_{2}\)?

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