
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 its center at the origin, with foci $F\_1$ and $F\_2$ on the $x$-axis. Point $P(2, \sqrt{3} )$ is on the ellipse, and the distances $|PF\_1 |$, $|F\_1 F\_2 |$, $|PF\_2 |$ form an arithmetic sequence. Determine the equation of the ellipse.

A) $\frac{{x}^{2}}{8}+ \frac{{y}^{2}}{6}=1$
B) $\frac{{x}^{2}}{16}+ \frac{{y}^{2}}{6}=1$
C) $\frac{{x}^{2}}{4}+ \frac{{y}^{2}}{2}=1$
D) $\frac{{x}^{2}}{8}+ \frac{{y}^{2}}{4}=1$

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