
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
$(1)$ Four different decorations need to be packed into a gift box. There are three different exquisite boxes to choose from. How many total packaging methods are there?<br/>$(2)$ Four different decorations need to be packed into a gift box. There are three different exquisite boxes to choose from. Each box must have at least one decoration. How many total packaging methods are there?<br/>$(3)$ Four different decorations need to be packed into a gift box. There are three identical exquisite boxes in terms of size, shape, and pattern to choose from. Each box must have at least one decoration. How many total packaging methods are there?<br/>$(4)$ Four different decorations need to be packed into a gift box. There are three identical exquisite boxes in terms of size, shape, and pattern to choose from. How many total packaging methods are there?

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