
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:
\[ \begin{array}{c@{}c@{\;}c@{}c@{}c@{}c}
& & & 5 & X & Y_{7} \\
&+& & & 5 & 2_{7} \\
\cline{2-6}
& & & 6 & 4 & X_{7} \\
\end{array} \]

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