Yes, he can choose Energy Explosion and Blades.

Thank you for the response!

Can he choose precision strike or steal energy?

There is no way in the game to make an attack without taking an action of some type, but he could potentially make an attack via a free action, move action, or power action. So I would say no.

Whoa, that makes him more useful,

@rpgambit, could you ask for a list of everything he can use?

I would agree. Precision Strike is triggered by an attack, and Steal Energy is triggered by a close combat attack. Neither requires an Action in their description, even though you will rarely, if ever, run into an circumstance when you can make an attack without an action.

Man, this is getting out of hand.

Precision Strike:
When this character makes an attack, it can’t be evaded, and the damage dealt can’t be reduced below 1 or transferred.

Steal Energy:
Each time an opposing character takes damage from a close combat attack made by this character, heal this character of 1 damage.

At first, I felt GL should only be able to use powers whose rules passage featured "Give this character a (power, ranged, or close-combat) action."

I thought BCF and EE were not on the table.

Now it makes sense. "When you give" is funtionally the same as "Give this character" for this power.

Now if someone can make a case for Precision Strike or Steal Energy, I will be flabbergasted.
The word "action" isn't even in the text. It could be argued these effects are by-products of said actions, but it seems a little flimsy.

If the argument exists for those, what about Shape Change?
It says activated by an action, would it have to even be his?
Shape Change
When this character is chosen as the target of an attack, you may roll a d6. On a result of 5 or 6, the attacker can’t target this character with an attack this turn and the attacker may choose another target character instead. The attacker then makes the attack unless there are no targets, in which case the action resolves without an attack.

Green Lantern could be targeted by an enemy using an Attack or Damage Power Ranged or Close Combat action. Shape Change could normally be used to avoid targeting by any attacks. Would GL's Shape Change then not be able to attempt avoidance of something like this:
TAIL ATTACK
Give Lizard a free action to make a close combat attack, modifying his attack value by -1.

No Power Ranged or Close Combat action given. No Shape Change for GL from this attack.
Could I pick Prob Con but only use it to affect rolls triggered by these actions?
Its getting a little wonky.

I don't think that any powers not starting with "when you give" or "give this character" will be options.