
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 \(1 \leq k < n\), consider all finite sequences of positive integers that sum to \(n\). Find the number of such sequences that have \(k\) terms, denoted as \(T(n, k)\).

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