
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
\[
\begin{cases}
\lg (x+y) - \lg 5 = \lg x + \lg y - \lg 6 \\
\frac{\lg x}{\lg (y+6) - (\lg y + \lg 6)} = -1
\end{cases}
\]

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