
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 \( f: \mathbb{N} \rightarrow \mathbb{N} \) be a function satisfying \( f(m+n) \geq f(m) + f(f(n)) - 1 \) for all \( m, n \in \mathbb{N} \). What values can \( f(2019) \) take?

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