You are a database expert and SQL optimizer. You will be given a SQL query and its rewritten variant. The rewritten query improves performance upon the original while maintaining equivalence. Your task is to create a new pair of original and rewritten queries that invoke a similar rewrite.

[ORIGINAL QUERY]```select promotions,total,cast(promotions as decimal(15,4))/cast(total as decimal(15,4))*100 from (select sum(ss_ext_sales_price) promotions from store_sales ,store ,promotion ,date_dim ,customer ,customer_address ,item where ss_sold_date_sk = d_date_sk and ss_store_sk = s_store_sk and ss_promo_sk = p_promo_sk and ss_customer_sk= c_customer_sk and ca_address_sk = c_current_addr_sk and ss_item_sk = i_item_sk and ca_gmt_offset = -7 and i_category = 'Home' and (p_channel_dmail = 'Y' or p_channel_email = 'Y' or p_channel_tv = 'Y') and s_gmt_offset = -7 and d_year = 2000 and d_moy = 12) promotional_sales, (select sum(ss_ext_sales_price) total from store_sales ,store ,date_dim ,customer ,customer_address ,item where ss_sold_date_sk = d_date_sk and ss_store_sk = s_store_sk and ss_customer_sk= c_customer_sk and ca_address_sk = c_current_addr_sk and ss_item_sk = i_item_sk and ca_gmt_offset = -7 and i_category = 'Home' and s_gmt_offset = -7 and d_year = 2000 and d_moy = 12) all_sales order by promotions, total limit 100;```

[REWRITTEN QUERY]```select promotions, total, (promotions / total) * 100 as promotion_percentage from ( select sum(case when p_channel_dmail = 'Y' or p_channel_email = 'Y' or p_channel_tv = 'Y' then ss_ext_sales_price else 0 end) as promotions, sum(ss_ext_sales_price) as total from store_sales join store on ss_store_sk = s_store_sk join promotion on ss_promo_sk = p_promo_sk join date_dim on ss_sold_date_sk = d_date_sk join customer on ss_customer_sk = c_customer_sk join customer_address on ca_address_sk = c_current_addr_sk join item on ss_item_sk = i_item_sk where ca_gmt_offset = -7 and i_category = 'Home' and s_gmt_offset = -7 and d_year = 2000 and d_moy = 12 ) as sales_data order by promotions, total limit 100;```

Now, consider the TPC-DS schema and create a new original and equivalent rewritten query pair such that the rewrite operation is similar to the provided demonstration.Keep the following points in mind while creating the new query pair:
1. The original query must contain CTEs.
2. The original query must make use of the following fact tables: ['inventory', 'catalog_sales']. Below is the join graph for these fact tables:
    ['inventory(inv_item_sk) references item(i_item_sk);', 'inventory(inv_warehouse_sk) references warehouse(w_warehouse_sk);', 'inventory(inv_date_sk) references date_dim(d_date_sk);']
    ['catalog_sales(cs_warehouse_sk) references warehouse(w_warehouse_sk);', 'catalog_sales(cs_ship_date_sk) references date_dim(d_date_sk);', 'catalog_sales(cs_ship_hdemo_sk) references household_demographics(hd_demo_sk);']
5. The original query must employ 4 joins.
6. The original query must employ the following aggregate functions: ['min'].
7. The original query must employ the following operators in its WHERE clause: ['sum', 'avg', 'count'].
8. The rewritten query must be equivalent to the original query, and must follow a similar rewrite pattern as in the given example. Enclose the original and rewritten queries within ``` and ```.