
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
Let $a$, $b$, $c$, and $d$ be digits such that $b = a + 2$, $c = a + 4$, and $d = a + 6$. Form the numbers $abcd$ and $dcba$, where these represent four-digit numbers created by these digits. What is the greatest common divisor of all numbers of the form $abcd + dcba$?

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