
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 \( a_1 \in \mathbb{Z}_{+} \) and \( a_1 \leq 18 \). Define the sequence \( \{a_n\} \) by:
\[
a_{n+1} = \begin{cases} 
2a_n, & \text{if } a_n \leq 18; \\
2a_n - 36, & \text{if } a_n > 18
\end{cases} \text{ for } n = 1, 2, \ldots.
\]
Find the maximum number of elements in the set \( M = \{a_n \mid n \in \mathbb{Z}_{+}\} \).

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