
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
The mascots "Bing Dung Dung" and "Xue Rong Rong" of the 2022 Beijing Winter Olympics and Paralympics are beloved by many. The Olympic official flagship store sells figurines and ornaments of "Bing Dung Dung" and "Xue Rong Rong." Two of the products are toy $A$ and ornament $B$, and their wholesale and retail prices are shown in the table below.

| Name | Toy $A$ | Ornament $B$ |
|------|---------|--------------|
| Wholesale Price (元/each) | $60$ | $50$ |
| Retail Price (元/each) | $80$ | $60$ |

$(1)$ If the flagship store wholesales a total of $100$ toys $A$ and ornaments $B$ for a total of $5650$元, how many toys $A$ and ornaments $B$ were wholesaled?

$(2)$ If the flagship store continues to wholesale a total of $100$ toys $A$ and ornaments $B$ (with wholesale and retail prices unchanged), and in order to make a profit of at least $1400$元 after selling all the wholesaled toys $A$ and ornaments $B, how many toys $A$ should the flagship store wholesale at least?

Present the answer in LaTex format: \boxed{Your answer}
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