To quickly review how "Navigate With the Navy" works: Selecting that mission will put you aboard a Navy ship about to set sail from either an island in the archipelago you're currently standing in or the island you're currently standing on. The ship will belong to the Navy associated with one of the two islands between which it is sailing. You will then take the wheel and perform Duty Navigation.
Can you choose which route to navigate with the Navy? No. You cannot.
Can you choose which Navy to navigate with? No. You cannot.
Can you see which navy route you'll get for any given click on "Navigate with the Navy" on the mission board? No. You generally can't do that either.
So why, you might wonder, would you ever want to use the Navy for memming LPs? Because it's the only way to access the Duty Navigation puzzle without either being an Officer in command of a ship or having been giving the order to navigate by an Officer. It also doesn't require you to buy or own a chart; the Navy have all they need on their ships' navigation tables.
Additionally, while Navigating with the Navy you will encounter no enemy ships to steal your goods nor spoil your chance at memming an LP.
(Remember, to have a chance to mem an LP you must approach it while stationed at the Duty Navigation puzzle without having turned about nor booched the puzzle during the previous league nor having been engaged in battle with another ship. Also, your Duty Report must grade you at Fine or better.)
So if you're after memming all the LPs you can from the Navies of a given archipelago, there are, roughly speaking, two basic ways to go about it:
- The Leisurely Completionist will hop aboard and simply stay aboard until they've memorized all routes possible with that Navy. Depending on whether they want to work on their stats or do something else (play in another client, browse the web, hop up and do the dishes), they'll either navigate continuously or only station up when it's a route they still need to finish memming.
- The Memmer in a Hurry will select the mission and evaluate the route it assigns. If it's one they've already memmed, they'll disembark and select the mission anew until they get one they've yet to memorize.
You'll probably end up doing a little from Column A and a little from Column B depending on how much free time you've got, how much of a multi-tasker you are, and how much you want to play right now. You'll have a different tolerance for idle time depending on whether you're jobbing in the weekend blockades in another YPP client or whether you've only got a half hour before you have to log out.
One final note here: If you are following the Way of the Memmer in a Hurry, don't be in too much of a hurry. Navy navigation routes only cycle so quickly. If you're clicking like lightning between your mission board and the island, you'll probably get the same route repeatedly, at least for a few minutes. Take a deep breath, wait for the Navy to announce the route ("We'll be setting sail in a moment for..."), then disembark.