
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 a straight line $L$ and a parabola $C: y^2 = 4x$ intersect at points $A$ and $B$, and the midpoint of the line segment $AB$ is $M(3, 2)$.
(Ⅰ) Determine the equation of line $L$.
(Ⅱ) Find the length of line segment $AB$.

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