Consider a buffer pool that can hold $4$ pages at a time. When a new page is requested and the buffer is full, the system applies the Least Recently Used $($LRU$)$ replacement policy to decide which page to evict.

The buffer pool's initial state is shown below, where each page is identified by its Page ID$,$ and the Last Used column represents the time when the page was last accessed. Each operation increases the current time by $1.$

Initial Buffer State:

Task:

Perform the following operations on the buffer pool and report the changes after each operation.

$(6$ Points for each operation$)$

Operations:

$1.$ Access Page $6$

$2.$ Access Page $3$

$3.$ Access Page $5$

$4.$ Access Page $8$

$5.$ Access Page $5$

For each operation, please answer:

$-$ Which frame is updated?

$-$ What are the Page ID and Last Used values of the updated frame?

Note:

$-$ Each operation depends on the result of the previous operation.

$-$ Use the LRU policy to evict the least recently used page if necessary.

$-$ Each operation increases the current time by $1.$