
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
A function $g$ from the integers to the integers is defined as follows:
\[g(n) = \left\{
\begin{array}{cl}
n + 5 & \text{if $n$ is odd}, \\
n/3 & \text{if $n$ is divisible by 3 and not by 2}, \\
n/2 & \text{if $n$ is divisible by 2}.
\end{array}
\right.\]
Suppose $m$ is odd and $g(g(g(m))) = 16.$ Find $m.$

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