
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 focus of the parabola $x^2 = 12y$ is $F$, and the line $l$ passing through the point $P(2, 1)$ intersects the parabola at points $A$ and $B$. If $P$ is the midpoint of $AB$, find the value of $|AF| + |BF|$.

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