
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 that the line passing through point $A(-1,0)$ intersects the parabola $C:y^{2}=2px\left(p \gt 0\right)$ at two distinct points $M$ and $N$, the line passing through point $M$ intersects $C$ at another point $Q$, the slope of line $MQ$ exists, and it passes through point $B(1,-1)$. The focus of the parabola $C$ is $F$, and the area of $\triangle ABF$ is $1$. <br/>$(Ⅰ)$ Find the equation of the parabola $C$. <br/>$(Ⅱ)$ Question: Does the line $QN$ pass through a fixed point? If it does, find the coordinates of the fixed point; if it does not, explain the reason.

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