
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 $\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a>b>0)$ with its left focus $F_1$, $O$ as the origin, point $P$ on the ellipse, and point $Q$ on the right directrix of the ellipse. If $\overrightarrow {PQ}=2 \overrightarrow {F_{1}O}$, $\overrightarrow {F_{1}Q}=\lambda \left( \frac { \overrightarrow {F_{1}P}}{| \overrightarrow {F_{1}P}|}+ \frac { \overrightarrow {F_{1}O}}{| \overrightarrow {F_{1}O}|}\right)(\lambda >0)$, then the eccentricity of the ellipse is $\boxed{\frac { \sqrt {5}-1}{2}}$．

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