
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
A parabola is given by the equation $y^2 = 4x$. A line $l$ with a slope angle of $\alpha$ passes through the focus $F$ of the parabola. The line $l$ intersects the parabola and its directrix at points $A$, $B$, and $C$ sequentially from top to bottom. Let $\lambda_1 = \frac{|AF|}{|BF|}$ and $\lambda_2 = \frac{|BC|}{|BF|}$. When $\alpha = \frac{\pi}{3}$, find the value of $(\lambda_1 + \lambda_2)$.

A) $3$
B) $4$
C) $5$
D) $6$

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