Combining two queries

I have a table called friends with a user_id and a friend_id (both of these
relate to an id in a users table).

For each friend relationship there are two rows. There are currently ONLY
reciprocal relationships. So if user ids 1 and 2 are friends there will be
two rows (1,2) and (2,1).

For 2 arbitrary ids, I need a query to get two pieced of data:
* Are the two users friends?
* How many friends do the two users have in common.

Is there a way to do this with one query? Currently I've only been able to
figure out how to do it with two.

SELECT
EXISTS(
SELECT 1
FROM friends
WHERE user_id = 166324 AND friend_id = 166325) AS friends,
(SELECT COUNT(1)
FROM friends f1 JOIN friends f2 ON f1.friend_id = f2.friend_id
WHERE f1.user_id = 166324 AND f2.user_id = 166325) AS mutual;

I'm wondering if there is a better way to do this using only one query.
I've tried a couple of GROUP BY approaches but they haven't worked.