
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 in integers: \(6x^{2} + 5xy + y^{2} = 6x + 2y + 7\)

Indicate the answer for which the value \(|x| + |y|\) is the largest. Write the answer in the form \((x; y)\).

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