
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 smallest value of $c$ such that the expression
\[
\log_{2005}(\log_{2004}(\log_{2003}(\log_{2002}{x})))
\]
is defined for all $x > c$.
A) $2002^{2004}$
B) $2003^{2004}$
C) $2002^{2003}$
D) $2003^{2002}$
E) $2004^{2003}$

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