
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
Find the ordered pair \((x, y)\) satisfying the equations:
\[
x + y = (3 - x) + (3 - y),
\]
\[
x - y = (x - 2) + (y - 2).
\]

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