
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. \( y \cdot x^{\log_{y} x} = x^{2.5} \)
2. \( \log_{3} y \cdot \log_{y}(y - 2x) = 1 \)

Solve for \( x \) and \( y \).

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