
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 $A$, $B$, and $C$ are all distinct digits less than $7$ (but non-zero) and the following calculation is true in base $7$. Find the sum of the values $A$, $B$, and $C$, expressing your answer in base $7$.
$$\begin{array}{c@{}c@{}c@{}c}
&A&B&C_7\\
+&B&C_7\\
\cline{2-4}
&A&C&A_7\\
\end{array}$$

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