Things I have done, which worked.
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**Praise.**  Maintaining a positive feedback and even slightly ridiculous congratulations whenever the player not 'does their turn faster' but 'takes a less optimal action'.  Whenever and wherever they take a less optimal action for roleplaying or other purposes, for speeding up the game or otherwise, tell them 'well done' or 'I like that' or something similar.  What is slowing them down is not 'a lack of speed', it's 'trying to calculate the most optimal action and running into difficulties'.  If taking less optimal actions is rewarded, they will feel less emotional impetus to try to find the optimal action, and thus will spend less time thinking about it/more often just go with whatever.

Doesn't work if you don't have a good grasp of what the person is considering as 'optimal', but it should be pretty obvious.  Works best if the whole group is doing this.

**Suggesting a course of action**.  'These gnolls are bunched together, so you could use your Fireball spell on this point here to get all of them'.  Suggestions work by far the best coming from the GM.  This works more by making it a committee decision (GM shoulders part of the blame if it 'goes wrong', which is always the underlying concern/fear) than by 'helping them with game mechanics they don't understand'.  Often they understand the game mechanics well enough to be going on with, the issue is trying to do 8 kinds of math in their head all at once in a rush.  The emotional support of the suggestion is the part that often is carrying the weight.

**Promise a lack of specific outcomes without player buy-in**.  Works only from the GM.  Take the player aside and tell them that specific outcomes (usually 'death' + 'fates worse than death') will not happen to their character unless they specifically tell you they are okay with that in a situation.  You won't ask them for confirmation, it just *won't happen* unless *they* come to you *first*.  This is kind of lame as part of the fun of D&D is the excitement of danger and death for 'your guy', but removing this as an outcome can cause some people to enjoy the game more as the possibility of character death limits their ability to interact with the game.

**In-game problems with obvious solutions**.  The Ice Imps are immune to cold but vulnerable to fire.  The Taunting Fey are invisible and have powerful mind attacks but are helpless if exposed.  The Old Witch has powerful curses that she can deliver through her many familiars, but if the familiars can't sneak up on the party at night the party can safely sleep.  Tailoring problems to specific capabilities the wizard has will potentially help him make decisions.  Resist the urge to tell him which spells to use though - obvious solution + suggest the solution can be a bit obvious.  Use this a few times to get the idea that 'monsters have counters' - doesn't need to be true for later monsters, but will put the guy in mindset of 'pick spell for monster' which isn't obvious sometimes, and shortcuts the 'hmm but what if I need See Invisibility later' roundabout thinking.  A clear, blindingly 'best' use for a spell gives context.  Don't use this forever - this is training wheels.

**Thematic development of character**.  Work out what *kind* of wizard this guy is playing.  Which arts were he trained in?  What magic did his mentor specialize in?  Perhaps he always was at odds because his natural affinities fell to Fire Magic and his mentor was an Enchanter.  Character development is fun, backstory development/flashbacks are fun, NPCs from a character's past coming into relevance in the current story is fun.  But more importantly, they can also be used to give cues to the player as to what options to select.  If he decides his mage has always liked mind magic, despite it being dubiously legal in the kingdom, it gives him a reason to cast Suggestion on the enemies instead of Firebolt.  That may help him come to faster decisions as to what to do on his turns, by adding a narrative element to the decision that isn't about 'what do I do/what if I do the wrong thing' etc.  If it's _for roleplaying reasons_, it can be sub-optimal.  Works well with the first option, Praise.  The GM will have to figure out some way to work in developing the character, from a brief discussion before/after a game to potentially having elements from the backstory come into the plot necessitating further character development.