
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
Given the parabola $y^{2}=2px (p > 0)$, a line passing through point $T(p,0)$ with a slope of $1$ intersects the parabola at points $A$ and $B$. Find the product of the slopes of lines $OA$ and $OB$, where $O$ is the coordinate origin.

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