
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 on a table face down with these conditions:
(a) all numbers are different,
(b) they sum to $15$,
(c) they are in increasing order from left to right.
Casey looks at the left card and claims uncertainty about the other two numbers. Tracy looks at the right card, also unable to deduce the remaining numbers. Stacy, viewing the middle card, makes a similar claim of uncertainty. Given that each relies on perfect reasoning and is aware of others' claims, identify the number on the middle card.
A) 4
B) 5
C) 6
D) 7

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