
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
An ellipse has the following optical property: a ray of light emitted from one focus reflects off the inner wall of the ellipse and then exactly passes through the other focus. Now, a ray of light is emitted from the left focus $F$ of the ellipse $\frac{x^2}{9} + \frac{y^2}{5} = 1$, reflects off the inner wall of the ellipse twice, and then returns to point $F$. The total distance traveled by the light ray is ______.

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