
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
Let \( a_{1}, a_{2}, \cdots, a_{k} \) be \( k \) distinct elements. Denote by \( R_{m}(n_{1}, n_{2}, \cdots, n_{k}) \) the number of ways to place \( n_{1} \) of \( a_{1} \), \( n_{2} \) of \( a_{2} \), ..., \( n_{k} \) of \( a_{k} \) into \( m \) distinct boxes such that no box is empty. Find the counting formula for \( R_{m}(n_{1}, n_{2}, \cdots, n_{k}) \).

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