
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
Find $X+Y$ (in base 10), given the following addition problem in base 7: 
\[ 
\begin{array}{c@{}c@{\;}c@{}c@{}c@{}c}
& & & 3 & X & Y_{7}\\ 
&+& & & 5 & 2_{7}\\ 
\cline{2-6}
& & & 4 & 2 & X_{7}\\ 
\end{array} 
\]

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