If $ABCDEFGH$ is a regular octagon, what do these vectors add to?

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\(ABCDEFGH\) is a regular octagon. Express in terms of a single vector the sum of the vectors

1. \(\mathbf{AC},\mathbf{AH},\mathbf{HG}\),

2. \(\mathbf{AB},\mathbf{AC},\mathbf{AF},\mathbf{AH},\mathbf{HG}\).

Given that \(\big \vert \mathbf{AB} \big \vert = 2,\) calculate \(\big \vert \mathbf{AF} \big \vert\).