
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 $S$, $H$, and $E$ be distinct digits where $S, H, E < 6$, and solve the following base-6 addition: $$\begin{array}{c@{}c@{}c@{}c} &S&H&E_6\\ &+&H&E_6\\ \cline{2-4} &H&E&H_6\\ \end{array}$$ What is the sum of $S$, $H$, and $E$ in base-6?

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