
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 $C: y^2 = 2px$ ($p > 0$) and a moving line $l: y = kx + b$ ($k, b$ are parameters, and $k \neq 0, b \neq 0$) that intersect at points $A(x_1, y_1)$ and $B(x_2, y_2)$, with $O$ being the origin of the Cartesian coordinate system. The slopes of lines $OA$ and $OB$ are $k_{OA}$ and $k_{OB}$ respectively, and it is given that $k_{OA} \cdot k_{OB} = \sqrt{3}$ always holds. Find the fixed point that line $l$ passes through as $k$ varies.

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