Try one of the following:

In a constituent type export, under the Last Action node, choose Action Date.  In the criteria window, at the bottom next to Date:, change the drop-down to Specific Range. Leave the Start date blank and make that End date equal to the As Of date. 
**With this method, the export criteria needs to be changed every time the As Of date changes.
Use this Last Action Date field in the Crystal Report.

or

In a constituent type export, under the Action node (not Last Action), choose Action Date.  Don't limit the date range.
In the Crystal Report, insert a group on the Prospect.
Next, create a date parameter to represent the As Of date in the report.
Then create a formula to calculate which Action Dates occurred before the As Of date:
    if {CnAct_1.CnAct_1_Action_Date} <= {?AsOfDate} then {CnAct_1.CnAct_1_Action_Date}
where {?AsOfDate} represents the parameter field created in an earlier step.
Place the formula in the Details section of the report.
Insert a Maximum of the formula per the Prospect group.  Doing a maximum will return the largest Action Date before the As Of date.  This will represent the Last Action as of an As Of date.