
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 $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 (a > 0, b > 0)$ with its right focus $F$, a line is drawn through point $F$ perpendicular to the $x$-axis, intersecting the two asymptotes at points $A$ and $B$, and intersecting the hyperbola in the first quadrant at point $P$. Let $O$ be the coordinate origin, and if $\overrightarrow{OP} = λ\overrightarrow{OA} + μ\overrightarrow{OB}$, with $λμ = \frac{4}{25} (λ, μ ∈ R)$, then the value of the eccentricity $e$ of the hyperbola is $\_\_\_\_\_\_$.

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