
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
Given the system of equations:
1. \( x + y = 12 \)
2. \( 2 \left( 2 \log_{y^2} x - \log_{1/x} y \right) = 5 \)

Find the values of \( x \) and \( y \).

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