
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 a strictly increasing function \( f: \mathbb{N}_{0} \rightarrow \mathbb{N}_{0} \) (where \( \mathbb{N}_{0} \) is the set of non-negative integers), which satisfies the relation \( f(n+f(m))=f(n)+m+1 \) for any \( m, n \in \mathbb{N}_{0} \). Find all possible values that \( f(2023) \) can take.

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