
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 $T$ be the sum of all positive real numbers $x$ for which 
\[
x^{3^{\sqrt 3}} = \sqrt{3}^{3^x}.
\]
Determine the nature of $T$.
A) $T < 2$
B) $2 \leq T < 4$
C) $4 \leq T < 6$
D) $T \geq 6$

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