
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
Define the function $g$ on positive integers as:
\[g(n) = \left\{
\begin{array}{cl}
n + 7 & \text{if $n < 7$}, \\
g(n - 3) & \text{if $n \ge 7$}.
\end{array}
\right.\]
Find the maximum value of the function $g$.

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