
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
Solve the system of equations: 
\[ \begin{cases} 
\lg (x-3) - \lg (5-y) = 0, \\
4^{-1} \cdot \sqrt[y]{4^{x}} - 8 \sqrt[x]{8^{y}} = 0.
\end{cases} \]

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