
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
Define functions \( f(n) \) and \( g(n) \) from the set of natural numbers \(\mathbf{N}\) to \(\mathbf{N}\) as follows:
\[ f(n) = \left\lfloor \frac{n(\sqrt{5}-1)}{2} \right\rfloor \]
\[ g(n) = \min \{ m \mid f(m) \geq n \} \]
where \( \lfloor x \rfloor \) denotes the greatest integer less than or equal to \( x \).

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