
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
Given the ellipse has its center at the origin, with foci $F_1$ and $F_2$ on the $x$-axis, and point $P(2, \sqrt{3})$ lies on the ellipse, if $|PF_1|$, $|F_1F_2|$, and $|PF_2|$ form an arithmetic sequence, find the equation of the ellipse.

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