
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 real numbers \( x \) and \( y \) that satisfy the following system of equations:
\[
\left\{
\begin{array}{l}
4^{-x} + 27^{-y} = \frac{5}{6}, \\
\log_{27} y - \log_{4} x \geq \frac{1}{6}, \\
27^{y} - 4^{x} \leq 1
\end{array}
\right.
\]

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