
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
The equation of the ellipse is $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ ($a > b > 0$). The left vertex of the ellipse is $A$, and the left and right foci are $F_{1}$ and $F_{2}$, respectively. $D$ is one endpoint on its minor axis. If $3\overrightarrow{DF_{1}} = \overrightarrow{DA} + 2\overrightarrow{DF_{2}}$, then the eccentricity of the ellipse is ______.

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