
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
There are four cards, each with one of the numbers $2$, $0$, $1$, $5$ written on them. Four people, A, B, C, and D, each take one card.

A says: None of the numbers you three have differ by 1 from the number I have.
B says: At least one of the numbers you three have differs by 1 from the number I have.
C says: The number I have cannot be the first digit of a four-digit number.
D says: The number I have cannot be the last digit of a four-digit number.

If it is known that anyone who has an even number is lying, and anyone who has an odd number is telling the truth, what is the four-digit number formed by the numbers A, B, C, and D have, in that order?

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