
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
The function $f(x)$, defined for $x \geq 0$, satisfies
\[f(x + y) = f(x) f(y)\]
for all $x, y \geq 0.$ Additionally, it is given that $f(3) = f(1)^3$. Find all possible values of $f(1)$.

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