
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
Pack 10 cigarette boxes into a rectangular or cubic shape in one go, ensuring the boxes touch each other tightly. Let the length, width, and thickness of a box be $a$, $b$, and $c$ respectively \( a > b > c \). Then:
1. How many different packaging methods are there? (Only consider the shape of the package)
2. Please write out the algebraic expression for the surface area of each packaging method.
3. Which packaging method has the smallest surface area? If $a=88\text{mm}, b=58\text{mm}, c=22\text{mm}$, what is the smallest surface area?

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