
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 \( m \) and \( n \) be positive natural numbers with \( m > n \). Define the sets \( A = \{1, 2, \ldots, m\} \) and \( B = \{1, 2, \ldots, n\} \). If \( C \subseteq A \), find the number of subsets \( C \) such that \( B \cap C \neq \varnothing \).

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