
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 a hyperbola has the vertices of $\triangle ABC$ as its foci, and passes through point $A$, with the sides opposite to the internal angles of $\triangle ABC$ being $a=4$, $b=5$, and $c=\sqrt{21}$, determine the eccentricity of this hyperbola.

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