
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 that $F_{1}$ and $F_{2}$ are the two foci of the ellipse $C$, and $P$ is a point on $C$. If $|PF_{1}|$, $|F_{1}F_{2}|$, and $|PF_{2}|$ form an arithmetic sequence, then the eccentricity of $C$ is ______.

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