
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 circle $x^2 + y^2 - 6x - 7 = 0$ and the parabola $C: y^2 = 2px$ ($p > 0$), whose directrix is tangent to the circle,
(Ⅰ) Find the equation of the parabola $C$.
(Ⅱ) A line passes through the focus $F$ of parabola $C$ and intersects the parabola at points $A$ and $B$. If $|AB| = 7$, 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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