
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 given equations:
\begin{align*}
3x - 2y &= (6 - 2x) + (6 - 2y), \\
x + 3y &= (2x + 1) - (2y + 1).
\end{align*}

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