
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
We have \( n \) objects to place in \( n \) positions. However, some objects are identical. There are \( k \) different types of objects, and there are \( n_{i} \) objects of the \( i^{\text{th}} \) type. Thus, \( \sum_{i=1}^{k} n_{i} = n \).

How many arrangements of these objects are there?

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