
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 $P$ be the sum of all positive real numbers $x$ for which \[ x^{3^{\sqrt{3}}} = 3^{3^x}. \] Determine the value of $P$.
A) \( P = \frac{3\sqrt{3}}{2} \)
B) \( P = \sqrt{3} \)
C) \( P = 3-1 \)
D) \( P = 9 \)
E) \( P > 3 \)

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