Find the sum of the terms of the Geometric Progression, $a+ar+ar^2 + ar^3 + \cdots$, where $a$ is the value of $x$ for which the function $7+2x \ln 25 -5^{x-1} - 5^{2-x}$ has a greatest value and $r$ is equal to $\displaystyle\lim_{x\rightarrow 0} \displaystyle\int_{0}^{x} \frac{t^2 dt}{x^2 \tan (π+x)}$

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