Can God Do Anything?

Isn't it true thatGod can't take illogical actions contradictory to His own character, such as make a rock that is too heavy for Him to lift?[Luke 1:37, Jeremiah 32:17, Jeremiah 32:27, Hebrews 6:18, Titus 1:2, James 1:13, 2 Timothy 2:13, Philippians 2:13].