
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 \(\mathbb{N}\) be the set of positive integers. Find all functions \(f: \mathbb{N} \rightarrow \mathbb{N}\) that satisfy the equation
\[ f^{abc-a}(abc) + f^{abc-b}(abc) + f^{abc-c}(abc) = a + b + c \]
for all \(a, b, c \geq 2\). (Here \(f^{k}\) means \(f\) applied \(k\) times.)

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