
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
For all non-negative integers \( x \) and \( y \), find all functions \( f: \mathbf{N} \rightarrow \mathbf{N} \) that satisfy \( f(3x + 2y) = f(x)f(y) \), where \(\mathbf{N}\) is the set of non-negative integers.

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