
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
Find all functions \( f: \mathbb{N}^{*} \rightarrow \mathbb{N}^{*} \) that satisfy:

\[
f^{abc-a}(abc) + f^{abc-b}(abc) + f^{abc-c}(abc) = a + b + c
\]

for all \( a, b, c \ge 2 \), where \( f^{k}(n) \) denotes the \(k\)-th composition of \( f \).

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