
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
Xiao Shi's mother needs to buy boxes to store 15 liters of food, and each box must be filled. There are two types of boxes, $A$ and $B$, with the capacity and price of a single box as shown in the table below:

| Type | $A$ | $B$ |
|------|-----|-----|
| Capacity (liters) | $2$ | $3$ |
| Price (yuan) | $13$ | $15$ |

$(1)$ Write down a purchasing plan that can be ________<br/>$(2)$ Just in time for the May Day holiday, type $A$ boxes are on sale. If you buy three or more at once, you can get a cashback of $10 yuan. The minimum cost required to buy the boxes is ________ yuan.

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