
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 $B$ (point $A$ is above the horizontal axis), and intersects the $x$-axis at point $F$. If $\overrightarrow{O F} = \lambda \overrightarrow{O A} + \mu \overrightarrow{O B}$, then $\mu^{2} - \lambda^{2} = \quad$ .

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