Reagan had the authority to send troops into conflict zones for up to 90 days without congressional approval as per the law (which is unconstitutional as the constitution gives the power to direct the military to the president).
War requires two branches of government: Congress to authorize it, and the President to direct the military. The president does not have authority to send troops without Congressional authorization. The 90 days you're referencing is the War Powers Resolution, and it's not a free 90 days to do whatever without Congressional authority.
Within 48 hours of deploying troops, the President must notify Congress of the troop deployments, and the troops must be recalled within 60 days, with a 30 day drawn down period, unless there is an authorization for the use of force from Congress or a declaration of war.
There are two ways then a president can violate the War Powers Resolution. By failing to notify Congress of troop deployments, or failing to recall within 60 days.
Partial list of instances in which a President has been accused of violating the War Powers Act:Reagan (Grenada)
Bush I (Panama)
Clinton (Haiti, Kosovo)
Bush II (Pakistan)
Obama (Pakistan, Yemen, Libya)
The thing is that these conflicts did not involve "war" with these countries but these were rather "conflicts". In theory the president could also recall the troops that are in the country we are at "conflict" with and send replacement troops for them to replace them; this would be very expensive but would still follow the letter (but not the spirit) of the law