Consider the following greedy strategy for finding a shortest path from vertex start to vertex goal in a given connected graph.

1: Initialize path to start.

2: Initialize set visited to {start}.

3: If start=goal, return path and exit. Otherwise, continue.

4: Find the edge (start,v) of minimum weight such that v is adjacent to start and v is not in visited.

5: Add v to path.

6: Add v to visited.

7: Set start equal to v and go to step 3.

Does this greedy strategy always find a shortest path from start to goal? Either explain intuitively why it works, or give a counterexample.