
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
Consider the parabola consisting of the points \((x, y)\) in the real plane satisfying
\[
(y + x) = (y - x)^2 + 3(y - x) + 3.
\]
Find the minimum possible value of \(y\).

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