
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 $\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1 (a > b > 0)$ with its left and right foci being $F_{1}(-c,0)$ and $F_{2}(c,0)$ respectively. If there exists a point $P$ on the hyperbola such that $\dfrac{\sin \angle PF_{1}F_{2}}{\sin \angle PF_{2}F_{1}}= \dfrac{a}{c}$, then the range of the eccentricity of this hyperbola is ______.

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