A frog makes $3$ jumps, each exactly $1$ meter long. The directions of the jumps are chosen independently at random. Find the probability that the frog's final position is no more than $1$ meter from its starting position. The original answer is in the form \(\frac{k}{m}\). Please give the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
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