
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
Given the sets \( A = \{1, 2, 3, \cdots, 99\} \), \( B = \{2x \mid x \in A\} \), and \( C = \{x \mid 2x \in A\} \), find the number of elements in \( B \cap C \).

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