1. A storage device comprising: a host interface configured to be connected to a host, the host interface receiving an invalidation instruction from the host; a memory including a first buffer and a second buffer; a nonvolatile memory; and a controller configured to: store, in the first buffer, a logical address range designated by the invalidation instruction, combine the stored logical address range with an internal logical address range stored in the second buffer, store the combined internal logical address range in the second buffer, and execute invalidation processing on the nonvolatile memory based on the combined internal logical address range.