
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 hyperbola \\(C_{1}\\): \\(\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1 (a > 0, b > 0)\\) and hyperbola \\(C_{2}\\): \\(\dfrac{x^{2}}{4} - \dfrac{y^{2}}{16} = 1\\) have the same asymptotes, and the right focus of \\(C_{1}\\) is \\(F(\sqrt{5}, 0)\\), then the equation of hyperbola \\(C_{1}\\) is \_\_\_\_\_\_.

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