
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
For the hyperbola $C_1$: $\frac{x^2}{3} - \frac{16y^2}{p^2} = 1$ where its left focus is on the directrix of the parabola $C_2$: $y^2 = 2px$ ($p > 0$), find the eccentricity of the hyperbola $C_1$.
A) $\frac{4}{3}$
B) $\sqrt{3}$
C) $\frac{2\sqrt{3}}{3}$
D) $4$

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