Complex SQL Scenario

Case1:Pick the max DATE1 if multiple distinct values.
Case2:If  no value or same value exists for DATE1 then pick maximum value from DATE2

SELECT
CLIENT_ID,
CASE 
WHEN COUNT(
DISTINCT  COALESCE(DATE1,TO_DATE('01-JAN-00','DD-MON-YY')))>1 
THEN MAX(DATE1) 
ELSE
MAX(DATE2)
END
FROM ADHOC
GROUP BY CLIENT_ID