
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
Distribute $n+m$ distinct objects $a_{1}, a_{2}, \cdots, a_{n}, a_{n+1}, \cdots, a_{n+m}$ among $n$ people $A_{1}, A_{2}, \cdots, A_{n}$ such that each person receives at least one object and $a_{i}(i=1,2, \cdots, n)$ cannot be given to $A_{i}$. Let the total number of different ways of distribution be $l(n, m)$. Find the counting formula for $l(n, m)$.

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