
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 \[x^{2^{x}} = 4^{x^2}.\] Determine the value of \(S\).
A) \(S = 1\) \\
B) \(S = 2\) \\
C) \(S = 3\) \\
D) \(S > 3\)

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