
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 hyperbola $$\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}=1(a＞0，b＞0)$$ with its left and right foci being F<sub>1</sub>（-c，0）and F<sub>2</sub>（c，0）respectively. If there exists a point P on the hyperbola such that $$\frac {sinPF_{1}F_{2}}{sinPF_{2}F_{1}}= \frac {a}{c}$$, then the range of the eccentricity of the hyperbola is \_\_\_\_\_\_.

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