
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 the hyperbola $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1 (a > 0, b > 0)$, the points $M$ and $N$ on the hyperbola are symmetrical to the origin, and point $P$ is a point on the hyperbola. The slopes of lines $PM$ and $PN$ are $k_1$ and $k_2$ respectively. If $k_1 \cdot k_2 = \dfrac{5}{4}$, determine the eccentricity of the hyperbola.

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