
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 \(x\) for which the expression
\[
\log_{2010}(\log_{2009}(\log_{2008}(\log_{2007}(x^{1/2}))))
\]
is defined, and find the smallest \(x\) for which this is true.
A) \(2007^2\)
B) \(2008^2\)
C) \(2009^2\)
D) \(2010^2\)

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