
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 that \( f(x) \) is a non-zero function defined on \(\mathbf{R}\), and for any \( a, b \in \mathbf{R}^{+} \), it satisfies \( f(1)=0 \) and \( f(a \cdot b) \geqslant a f(b) + b f(a) \). Determine the relationship between \( f\left(a^{n}\right) \) and \( f(a) \).

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