A random walk...

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Tianbo is bored, and he decides he will accept his friend's challenge and play a game of life and death on the number line. At the beginning, he stands at the origin and blindfolds himself, and every second afterwards, he moves one unit to the left with probability \(\frac{16}{25}\) and one unit to the right with probability \(\frac{9}{25}\). If Tianbo arrives back at the origin, he dies. The probability that he survives can be expressed as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are relatively prime. Determine \(a+b\).

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