
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
Given \( m_{1} \) instances of \( 1 \), \( m_{2} \) instances of \( 2 \), ..., \( m_{n} \) instances of \( n \) arranged in any sequence from left to right. How many ways are there to arrange them such that each \( k+1 \) appears only after at least one \( k \) has appeared? (where \( k = 1, 2, ..., n-1 \)).

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