
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
Given: x + y = 5, (x-2)(y-2) = -3. Find the values of the following algebraic expressions:
1. xy;
2. x^2 + 4xy + y^2;
3. x^2 + xy + 5y.

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