
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 $X = \{1, 2, \cdots, 100\}$. Let $A$ be a subset of $X$. If for any two elements $x$ and $y$ in $A$ with $x < y$, it holds that $y \neq 3x$, find the maximum value of $|A|$.

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