
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
Consider the parabola $y^2 = 4x$. A line with slope 1 is drawn through its focus $F$, intersecting the parabola at points $A$ and $B$. If $\overrightarrow{AF} = \lambda \overrightarrow{FB}$ for some $\lambda > 1$, find the value of $\lambda$.

A) $\sqrt{2} + 1$
B) $\sqrt{3} + 1$
C) $\sqrt{5} + 1$
D) $2\sqrt{2} + 3$

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