
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 $A$, $B$, and $C$ be distinct digits where $A < 7$, $B < 7$, and $C < 7$. Suppose we have ${AB_7} + {C_7} = {C}0_7$ and ${AB_7} + {BA_7} = {CC_7}$. Find the three-digit number ${ABC}$.

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