
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 set of $x$-values that satisfy the equation $x^{\log_{10}(x^2)} = \frac{x^4}{1000}$.
- **A)** 10
- **B)** 31.6227766
- **C)** 10 or 31.6227766
- **D)** more than two real numbers

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