
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 $C$: $y^{2}=12x$, a line $l$ passes through point $P(2,0)$ with a slope of $1$, and intersects the parabola $C$ at points $A$ and $B$. Find the distance from the midpoint of line segment $AB$ to the axis of symmetry of parabola $C$.

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