
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
Three cards, each with a positive integer, are placed face-down on a table. The numbers are all different, they sum to $15$, and are in increasing order from left to right. Casey looks at the number on the leftmost card and states, "I don't have enough information to determine the other two numbers." Tracy looks at the number on the rightmost card and declares, "I don't have enough information to determine the other two numbers." Lastly, Stacy looks at the number on the middle card and announces, "I don't have enough information to determine the other two numbers." Assuming each participant reasons perfectly and hears the others' comments, what number is on the middle card?
A) 3
B) 4
C) 5
D) 6

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