
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 that the foci of a hyperbola are located on the $x$-axis with a focal distance of $2 \sqrt {5}$, and one of its asymptotes is parallel to the line $x-2y+1=0$, determine the standard equation of the hyperbola.

A) $\dfrac {x^{2}}{4}-y^{2}=1$
B) $x^{2}- \dfrac {y^{2}}{4}=1$
C) $\dfrac {3x^{2}}{20}- \dfrac {3y^{2}}{5}=1$
D) $\dfrac {3x^{2}}{5}- \dfrac {3y^{2}}{20}=1$

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