
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
\[
\left\{
\begin{array}{l}
3^{1+2 \log _{3}(y-x)}=48, \\
2 \log _{5}(2 y-x-12)-\log _{5}(y-x)=\log _{5}(y+x) .
\end{array}
\right.
\]

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