
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 the universal set $U = \{1, 2, 3, 4, 5, 6\}$. Subsets of $U$ can represent 6-digit binary strings composed of 0s and 1s. For example, the subset $\{2, 4\}$ represents the 6-digit binary string $010100$, where the 2nd and 4th characters are 1, and all others are 0. The empty set represents the string $000000$. If $A = \{1, 3\}$, and the binary string represented by $A \cup B$ is $101001$, then the number of subsets $B$ that satisfy this condition is $\boxed{4}$.

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