
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
Determine the set of all real numbers $y$ such that the expression
\[
\log_{2010}(\log_{2005}(\log_{2008}(y)))
\]
is well-defined.
$\textbf{A)}\ 2005 \qquad \textbf{B)}\ 2008^{2005} \qquad \textbf{C)}\ 2010^{2008} \qquad \textbf{D)}\ 2005^{2008}$

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