
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 a parabola $C$: ${y}^{2}=2px (p > 0)$ and a variable line $l$: $y=kx+b (k, b$ are variables, and $k \ne 0$, $b \ne 0)$, intersecting at points $A$ and $B$. In a rectangular coordinate system with origin $O$, the slopes of lines $OA$ and $OB$ are denoted as ${k}_{1}$ and ${k}_{2}$, respectively. If ${k}_{1} \cdot {k}_{2}=\sqrt{3}$ holds true, find the coordinates of the fixed point through which line $l$ passes as $k$ varies.

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