
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 the values of \( x \) and \( y \) that satisfy the following system of equations, given that \( a < 0 \):

\[ 
\begin{cases} 
xy = a^2 \\ 
\lg^2(x) + \lg^2(y) = 2.5 \lg^2(a^2)
\end{cases} 
\]

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