
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 smallest integer $d$ for which the expression:
\[
\log_{2010}(\log_{2009}(\log_{2008}(\log_{2007}{x})))
\]
is defined for all $x > d$.
A) $2007^{2008}$  
B) $2007^{2009}$  
C) $2009^{2010}$  
D) $2010^{2011}$  
E) $2007^{2010}$

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