ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: YES)

[Francises Sun]

I am newbie to mysql and installed mysql 5.6 server/client rpm on a test box.

I did following steps:

[root@oracle01 mysql]# service mysql stop
Shutting down MySQL.. [ OK ]
[root@oracle01 mysql]# /usr/bin/mysqld_safe --skip-grant-tables
130921 08:14:16 mysqld_safe Logging to '/var/lib/mysql/oracle01.err'.
130921 08:14:16 mysqld_safe Starting mysqld daemon with databases from /var/lib/mysql

on another shell, I did following:

mysql> use mysql
Reading table information for completion of table and column names
You can turn off this feature to get a quicker startup with -A

Database changed
mysql> show databases;
+--------------------+
| Database |
+--------------------+
| information_schema |
| mysql |
| performance_schema |
| test |
+--------------------+
4 rows in set (0.00 sec)

mysql> update user set password=123456 where user="root";
Query OK, 0 rows affected (0.00 sec)
Rows matched: 4 Changed: 0 Warnings: 0

mysql> flush privileges;

[2]+ Stopped /usr/bin/mysqld_safe --skip-grant-tables
[root@oracle01 mysql]# mysql -u root -p
Enter password:
ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: YES)


ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: YES)

Please help me to loginto mysql.

Thank you in advance.