
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 line passes through the right focus of the ellipse $C: \frac{x^2}{6} + \frac{y^2}{2} = 1$ and has a slope angle of $\frac{\pi}{3}$. The length of the chord it cuts from the ellipse $C$ is ______.

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