
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 line $\sqrt{3}x - y - \sqrt{3} = 0$ intersects the parabola $y^2 = 4x$ at points $A$ and $B$ (with $A$ being above the x-axis), and intersects the x-axis at point $F$. If $\overrightarrow{OF} = \lambda \overrightarrow{OA} + \mu \overrightarrow{OB}$, then $\mu^2 - \lambda^2 = \qquad$.

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