
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 $\dfrac {x^{2}}{a^{2}} - \dfrac {y^{2}}{b^{2}} = 1$ represents a hyperbola with left and right foci $F_1$ and $F_2$, and asymptotes $l_1$ and $l_2$. A point P in the first quadrant lies on $l_1$. If $l_2$ is perpendicular to the line segment PF_1 and parallel to the line segment PF_2, determine the eccentricity of the hyperbola.

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