
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 \( 0 \leq k \leq n \) be integers (with \( (k, n) \neq (0,0) \)). Then:

\[ 
\binom{n}{k} = \binom{n-1}{k} + \binom{n-1}{k-1} 
\]

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