
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 \[ f(x) = \left\{ 
\begin{array}{cl} 
x^3 & \text{ if } x \leq 3, \\
\sqrt[3]{x} & \text{ if } x > 3.
\end{array} 
\right. \]
Find $f(f(f(1)))$.

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