
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
Suppose that \( x_{1} \) and \( x_{2} \) are the two roots of the equation \( (x-2)^{2} = 3(x+5) \). What is the value of the expression \( x_{1} x_{2} + x_{1}^{2} + x_{2}^{2} \) ?

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