
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 $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$, let $d_{1}$, $d_{2}$ be the distances from any point on the ellipse to its two foci, and $2c$ be the focal length. If $d_{1}$, $2c$, $d_{2}$ form an arithmetic sequence, find the eccentricity of the ellipse.

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