
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
In the Cartesian coordinate system $xOy$, the graph of the parabola $y=ax^2 - 3x + 3 \ (a \neq 0)$ is symmetric with the graph of the parabola $y^2 = 2px \ (p > 0)$ with respect to the line $y = x + m$. Find the product of the real numbers $a$, $p$, and $m$.

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