
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 $f(n) > 0$ ($n \in \mathbb{N}^*$), $f(1) = 3$, and for any $n_1, n_2 \in \mathbb{N}^*$, $f(n_1 + n_2) = f(n_1)f(n_2)$. Guess an analytical expression for $f(n)$, which is $f(n) = \ $.

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