
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 left vertex of the ellipse $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$ is $A$, the right focus is $F$, the upper vertex is $B$, and the lower vertex is $C$. If the intersection point of line $AB$ and line $CF$ is $(3a,16)$, then the standard equation of the ellipse is _____ .

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