
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
If $P$, $Q$, and $R$ are distinct non-zero digits less than 6, and the following addition is true, find the sum of the three values $P$, $Q$, and $R$, expressing your answer in base $6$. 
$$
\begin{array}{c@{}c@{}c@{}c}
 &P&Q&R_6\\
 &+&Q&R_6\\
\cline{2-4}
 &P&R&P_6\\
\end{array}
$$

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