
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 \[g(x) = \left\{
\begin{array}{cl}
x^3 &\text{ if } x > 2, \\
2x &\text{ if } x \le 2.
\end{array}
\right.\] Find $g(g(g(1)))$.

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