A bug starts at a vertex of a grid made of equilateral triangles of side length \(1\). At each step, the bug moves in one of the \(6\) possible directions along the grid lines randomly and independently with equal probability. What is the probability that after \(5\) moves the bug never will have been more than \(1\) unit away from the starting position? Provide your answer as a fraction in simplest form \(\frac{k}{m}\), and calculate the value of \(k + m\).

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