
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
Suppose $A$, $B$, $C$, and $D$ are non-zero distinct digits less than $5$. Suppose we are given ${AB_5} + {C_5} = {D}0_5$ and ${AB_5} + {BA_5} = {DD_5}$. Find the four-digit number ${ABCD}$. (Interpret these as base-5 numbers.)

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