
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
Red Star Fruit Store wholesales fruits for retail. The wholesale and retail prices of loquat, cherries, and apples are as follows:

| Fruit Type | Loquat | Cherries | Apples |
|------------|--------|----------|--------|
| Wholesale Price (元/$/kg) | $m$ | $n$ | $12$ |
| Retail Price (元/$/kg) | $10$ | $42$ | $16$ |

It is known that the wholesale price of loquat is $28$ yuan cheaper per kilogram than cherries. If the fruit store wholesales $80$ kilograms of loquat and $120$ kilograms of cherries for $4960$ yuan,

$(1)$ Find the values of $m$ and $n$;

$(2)$ If the store wholesales loquat, cherries, and apples for $5280$ yuan, with loquat and apples totaling $160$ kilograms, and after selling out all the fruits that day, they earn no less than $1120$ yuan, what is the maximum amount of loquat the store can wholesale?

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