
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 $C:y^{2}=2px\left(p \gt 0\right)$ with the focus $F$, a line $l$ passing through point $F$ with an inclination angle of $θ=\frac{{π}}{3}$ intersects $C$ at points $A$ and $B$, where $O$ is the origin. If the area of $\triangle AOB$ is ${S_{△AOB}}=12\sqrt{3}$, then find the distance from the midpoint $M$ of segment $AB$ to the $y$-axis.

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