Optimize mysql query using various join and order by rand() - mysql

Question

I was having trouble on my site, so I went look into mysql slow query log.
Fixed some indexing and also querys without joins now the server load got lower and its running fine.
I still have a query that I havent been able to fix, if any of you have a tip so I can make it better, I would appreciated it.
This is the query
SELECT p.product_id,
p.product_offer_price,
ps.subcategory_name,
pb.brand_name,
pm.model_name,
pm.display_name,
pm.year_from,
pm.year_to
FROM product p
INNER JOIN product_subcategory ps ON ps.subcategory_id = p.product_subcategory_id AND ps.subcategory_category_id = 12
INNER JOIN product_stock pq ON pq.product_id = p.product_id AND pq.product_quantity > 0
INNER JOIN product_photos pp ON pp.product_id = p.product_id
INNER JOIN product_brand pb ON pb.brand_id = p.product_brand_id
INNER JOIN product_model pm ON pm.model_id = p.product_model_id
GROUP BY p.product_id
ORDER BY RAND() LIMIT 4;
This is what explain shows about the query
I was trying to accomplish something like this, but doesn't work
SELECT p.product_id, p.product_offer_price, ps.subcategory_name, pb.brand_name, pm.model_name, pm.display_name, pm.year_from, pm.year_to
FROM product p
INNER JOIN product_subcategory ps ON ps.subcategory_id = p.product_subcategory_id
AND ps.subcategory_category_id =12
INNER JOIN product_stock pq ON pq.product_id = p.product_id
AND pq.product_quantity >0
INNER JOIN product_photos pp ON pp.product_id = p.product_id
INNER JOIN product_brand pb ON pb.brand_id = p.product_brand_id
INNER JOIN product_model pm ON pm.model_id = p.product_model_id
WHERE p.product_id >= FLOOR( 1 + RAND( ) * (
SELECT MAX( product_id )
FROM product ) )
GROUP BY p.product_id
LIMIT 4