
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
Let \( S \) be the sum of all positive real numbers \( x \) for which
\[
x^{3^{\sqrt{3}}} = \sqrt{3}^{3^x}.
\]
Determine \( S \).
A) \( S < \sqrt{3} \)   
B) \( S = \sqrt{3} \)  
C) \( \sqrt{3} < S < 2 \)  
D) \( 2 \le S < 6 \)  
E) \( S \ge 6 \)

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