
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
\[
\log_{2010}(\log_{2009}(\log_{2008}(\log_{2007}(\log_{2006}{x}))))
\]
is defined, which is $\{x\mid x > c\}$. What is the value of $c$?
A) $2006^{2007}$
B) $2006^{2008}$
C) $2006^{2007^{2008}}$
D) $2007^{2008^{2009}}$

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