
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 \(\mathbb{Z}_{\geqslant 0}\) be the set of all nonnegative integers. Find all the functions \( f: \mathbb{Z}_{\geqslant 0} \rightarrow \mathbb{Z}_{\geqslant 0} \) satisfying the relation
$$
f(f(f(n)))=f(n+1)+1
$$
for all \( n \in \mathbb{Z}_{\geqslant 0} \).

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