Argument * can only be used in COUNT(*)

My table looks like this:

examID action   timeSinceStart
a     write     300
a     answer   2535
b     answer   3834
a     answer   2900
c     write     774
d     edit     3674
c     answer   3489
a     edit     3983
c     answer    300

I seek the following output:

examID averageTime
a      2717.5
b      3834
c      1894.5    

That is, I only look at the actions that are answer, I only write the examID once and another column with the average time since start at the point of answering.

Is it possible to do this directly without creating a column for the sum and a column for the count, and then writing the average formula?

My "complicated" approach doesn't work:

%%bigquery df_average_times
SELECT countTimes.examID, sumTimes.answerSum, countTimes.answerCount, (sumTimes/countTimes) as averageTime
FROM
 ( SELECT examID, timeSinceStart, action, SUM(*) as answerSum
 FROM `some-database.bq.results` 
 GROUP BY examID, timeSinceStart, action
 HAVING action='answer'
 ORDER BY examID) as sumTimes
 INNER JOIN
 ( SELECT examID, timeSinceStart, action, COUNT(*) as answerCount
 FROM `some-database.bq.results` 
 GROUP BY examID, timeSinceStart, action
 HAVING event='answer'
 ORDER BY examID) as countTimes
 ON falseAnswers.questionId = trueAnswers.questionId

The error states:

ERROR:
 400 Argument * can only be used in COUNT(*) at [3:58]

I think you need below query -

SELECT examID, AVG(timeSinceStart)
  FROM (SELECT examID, timeSinceStart
          FROM `some-database.bq.results`
         WHERE action='answer') X
 GROUP BY examID;