
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 distinct digits $a$, $b$, $c$, and $d$ (none consecutive and all different) are selected to form the four-digit numbers $abcd$ and $dcba$. What is the greatest common divisor (GCD) of all possible numbers of the form $abcd+dcba$, considering $a, b, c, d$ non-consecutive and distinct?

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