
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 \( f, g: \mathbf{N} \rightarrow \mathbf{N} \) with \( f(n) = 2n + 1 \) and \( g(1) = 3 \), and the condition
$$
g(n) \geq f[g(n-1)], \forall n \geq 2,
$$
find \( g(n) \).

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