
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 \( n, k \in \mathbb{N}^{*} \). Calculate the number of solutions \( \left(a_{1}, \ldots a_{k}\right) \in \left(\mathbb{N}^{*}\right)^{k} \) for the equation \( a_{1}+\cdots+a_{k}=n \). Calculate the number of solutions \( \left(a_{1}, \ldots a_{k}\right) \in \mathbb{N}^{k} \) for the equation \( a_{1}+\cdots+a_{k}=n \).

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