
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
On the ellipse $\frac {x^{2}}{4}+ \frac {y^{2}}{2}=1$, for any point P, Q is symmetric to P about the x-axis. If $\overrightarrow {F_{1}P}\cdot \overrightarrow {F_{2}P}≤1$, then the range of the angle between $\overrightarrow {F_{1}P}$ and $\overrightarrow {F_{2}Q}$ is _____.

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