
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 Li plans to make two rectangular paper boxes of different sizes using cardboard on the weekend, with the following dimensions: (unit: centimeters)

|         | Length | Width | Height |
|---------|--------|-------|--------|
| Small Box | $a$ | $b$ | $c$ |
| Large Box | $2a$ | $2b$ | $1.5c$ |

$(1)$ How much square centimeters of cardboard are needed to make these two boxes together?  
$(2)$ How many more square centimeters of cardboard are needed to make the large box compared to the small box?  
$(3)$ If the cardboard costs $15$ yuan per square meter, when $a=20$, $b=10$, $c=15$, how much does it cost to make the two boxes?

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