
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 two points $F_1(-1,0)$ and $F_2(1,0)$, and $|F_1F_2|$ is the arithmetic mean of $|PF_1|$ and $|PF_2|$, find the equation of the locus of the moving point $P$. The options are:
A) $\frac{x^2}{16}+\frac{y^2}{9}=1$
B) $\frac{x^2}{16}+\frac{y^2}{12}=1$
C) $\frac{x^2}{4}+\frac{y^2}{3}=1$
D) $\frac{x^2}{3}+\frac{y^2}{4}=1$

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