
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 system of equations:
\[ \begin{cases} 9y^2 - 4x^2 = 144 - 48x, \\ 9y^2 + 4x^2 = 144 + 18xy. \end{cases} \]

After obtaining the solutions \(\left(x_1, y_1\right), \left(x_2, y_2\right), \ldots, \left(x_n, y_n\right)\), write the sum of the squares of the solutions:
\[ x_1^2 + x_2^2 + \ldots + x_n^2 + y_1^2 + y_2^2 + \ldots + y_n^2. \]

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