
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
Four cards, each with a positive integer written on it, are lying face-down on a table. Dennis, Mandy, Sandy, and Randy are told that:
(a) the numbers are all distinct,
(b) they sum to $30$, and
(c) they are in increasing order, left to right.
First, Dennis looks at the number on the leftmost card and claims, "I cannot determine the other three numbers." Next, Mandy, who sees the second card from the left, claims, "I also cannot determine the other three numbers." Following Mandy, Sandy sees the third card from the left and says, "I too cannot determine the remaining numbers." Finally, Randy, after looking at the rightmost card, comments, "I am also unable to determine the other three numbers." Assume all parties deduce logically and are privy to previous comments. What number is on the second card from the left?
A) 2
B) 3
C) 4
D) 5
E) 6

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