
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 Double 11 online promotion event is coming soon. Two online stores, Store A and Store B, sell two types of heaters, Type A and Type B, with the following retail prices and shipping costs:<br/>

| Model/Store | Type A | Type B | Shipping Cost Type A | Shipping Cost Type B |
|-------------|--------|--------|----------------------|----------------------|
| Store A     | $100$ per unit | $200$ per unit | $10$ per unit | $10$ per unit |
| Store B     | $120$ per unit | $190$ per unit | Free | $12$ per unit |

A certain company plans to purchase a total of $100$ units of Type A and Type B heaters online, with $x$ units of Type A heaters to be purchased.<br/>

$(1)$ If both types of heaters are purchased from Store A, the total cost will be ______ yuan (expressed in the simplest form containing $x$);<br/>
If both types of heaters are purchased from Store B, the total cost will be ______ yuan (expressed in the simplest form containing $x$);<br/>
$(2)$ When $x=60$, solve the following problems by calculation:<br/>
① Under the conditions in $(1)$, which online store is more cost-effective for the company to purchase heaters from?<br/>
② If both types of heaters can be freely chosen and purchased from both online stores, is there a more favorable option than in ①? If so, write down this option and calculate the total cost of purchasing heaters at this time. If not, please explain the reason.

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