
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 positive integers \( N \) and \( k \), we counted how many different ways the number \( N \) can be written in the form \( a + b + c \), where \( 1 \leq a, b, c \leq k \), and the order of the summands matters. Could the result be 2007?

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