
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
Real numbers \( x \) and \( y \) satisfy the following equations:
\[
\begin{array}{l}
x=\log_{10}\left(10^{y-1}+1\right)-1 \\
y=\log_{10}\left(10^{x}+1\right)-1
\end{array}
\]
Compute \( 10^{x-y} \).

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