
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 \( M = \{1, 2, \cdots, 65\} \) and \( A \subseteq M \) be a subset. If \( |A| = 33 \) and there exist \( x, y \in A \) with \( x < y \) such that \( x \mid y \), then \( A \) is called a "good set". Find the largest \( a \in M \) such that every 33-element subset containing \( a \) is a good set.

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