Can the Reaction trigger along with the battle action on this strategy
EaW: Strategy Precision
A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
Can the Reaction trigger along with the battle action on this strategy
Assuming you mean, can I use both the Battle action and the Reaction on a single copy of Precision, no. According to the sequence for playing Strategies, by default a Strategy card must be in your hand to use it's abilities.
By the time the trigger for the Reaction on Precision is reached by the Battle action on Precision in Step B, the card is no longer in your hand (having been placed in the temporary resolution area for that card during Step A).
If you have multiple copies of Precision in hand, there is nothing preventing you from using one for it's Battle action and then using the other copy for the Reaction.
On: Precision