
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 real numbers \(x\) for which
\[
\log_{1005}(\log_{1004}(\log_{1003}(\log_{1002}{x})))
\]
is defined and represent it in the form \(\{x\mid x > c\}\). What is the value of \(c\)?
A) \(1002\)  
B) \(1002^2\)  
C) \(1002^{1003}\)  
D) \(1002^{1004}\)  
E) \(1003\)

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