
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
The parabola $C$: $y^2 = 2px$ ($p > 0$) has a point $M(x, y)$ whose distance to the directrix is $x + 2$.

(I) Find the value of $p$;

(II) Suppose a line $l$ passing through the focus $F$ of the parabola $C$ intersects $C$ at points $A(x_1, y_1)$ and $B(x_2, y_2)$. Find the value of $y_1 \cdot y_2$.

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