
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 that \(S\), \(H\), and \(E\) are all distinct non-zero digits less than 6, and the following equation holds true in base 6:
$$\begin{array}{c@{}c@{}c@{}c}
  & S & H & E_6 \\
+ & E & S & H_6 \\
\hline
  & H & E & S_6 \\
\end{array}$$
Find the sum of the values \(S\), \(H\), and \(E\) expressed in base 6.

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