
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 non-zero digits less than or equal to 6. Solve the following equation in base 7:
$$\begin{array}{c@{}c@{}c@{}c}
 &A&B&C_7\\
+&B&C_7\\
\hline
&A&C&A_7\\
\end{array}$$
Find the sum of $A$, $B$, and $C$ in base 7.

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